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%!PS-Adobe-2.0 %%Creator: dvips(k) 5.92a Copyright 2002 Radical Eye Software %%Title: w2.dvi %%Pages: 9 %%PageOrder: Ascend %%BoundingBox: 0 0 596 842 %%DocumentFonts: CMBX12 CMSY10 CMR10 CMMI10 CMR12 LCIRCLE10 LINE10 %%+ MSBM10 CMMI12 CMR7 CMMI7 CMEX10 CMSY7 CMTI12 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -o w2.ps w2.dvi %DVIPSParameters: dpi=600, compressed %DVIPSSource: TeX output 2005.12.09:0842 %%BeginProcSet: texc.pro %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round 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cleartomark %%EndFont %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-15 -951 1252 782}readonly def /UniqueID 5000817 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 8 /braceleftbig put dup 9 /bracerightbig put dup 26 /braceleftbigg put dup 27 /bracerightbigg put dup 88 /summationdisplay put dup 110 /braceleftBig put dup 111 /bracerightBig put readonly def /FontBBox{-24 -2960 1454 772}readonly def /UniqueID 5000774 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-29 -960 1116 775}readonly def /UniqueID 5000820 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{0 -250 1171 750}readonly def /UniqueID 5087382 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-27 -250 1122 750}readonly def /UniqueID 5000790 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF5B8CABB9FFC6CC3F1E9AE32F234EB60FE7D E34995B1ACFF52428EA20C8ED4FD73E3935CEBD40E0EAD70C0887A451E1B1AC8 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.001) readonly def /Notice (Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved) readonly def /FullName (LINE10) readonly def /FamilyName (LaTeX) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /LINE10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 64 /a64 put readonly def /FontBBox{-150 -150 1020 1020}readonly def /UniqueID 5011940 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: LCIRCLE10 %!PS-AdobeFont-1.1: LCIRCLE10 1.001 %%CreationDate: 1992 Oct 23 20:21:59 %%RevisionDate: 2001 Jun 05 20:21:59 % Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.001) readonly def /Notice (Copyright (C) 1997, 2001 American Mathematical Society. All Rights Reserved) readonly def /FullName (LCIRCLE10) readonly def /FamilyName (LaTeX) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /LCIRCLE10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 113 /a113 put dup 115 /a115 put readonly def /FontBBox{-2000 -2000 2040 2040}readonly def /UniqueID 5011942 def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-34 -251 988 750}readonly def /UniqueID 5000794 def currentdict end currentfile eexec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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-251 -250 1009 969}readonly def /UniqueID 5000793 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5CF7158F1163BC1F3352E22A1452E73FECA8A4 87100FB1FFC4C8AF409B2067537220E605DA0852CA49839E1386AF9D7A1A455F 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0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMBX12 %!PS-AdobeFont-1.1: CMBX12 1.0 %%CreationDate: 1991 Aug 20 16:34:54 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMBX12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Bold) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMBX12 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /.notdef put readonly def /FontBBox{-53 -251 1139 750}readonly def /UniqueID 5000769 def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F D2DECBA99459A4C59DF0C6EBA150284454E707DC2100C15B76B4C19B84363758 469A6C558785B226332152109871A9883487DD7710949204DDCF837E6A8708B8 2BDBF16FBC7512FAA308A093FE5F0364CD5660F74BEE96790DE35AFA90CCF712 B1805DA88AE375A04D99598EADFC625BDC1F9C315B6CF28C9BD427F32C745C99 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4317 y(w)m(e)39 b(will)e(call)g(it)h(the)h(c)m(haracter)e(of)h(the)h (algebra.)404 4703 y(Suc)m(h)53 b(algebras)f(naturally)f(app)s(ear)h (when)i(w)m(e)f(study)g(n-tuples)g(of)257 4852 y(self-adjoin)m(t)37 b(op)s(erators)f(with)i(giv)m(en)g(sp)s(ectra)g(suc)m(h)h(that)1248 5101 y Fg(A)1336 5119 y Fn(1)1408 5101 y Fl(+)26 b Fg(A)1613 5119 y Fn(2)1685 5101 y Fl(+)h Fg(:::)e Fl(+)i Fg(A)2133 5119 y Fm(n)2220 5101 y Fl(=)33 b Fg(\015)7 b(I)i(:)1852 5637 y Fk(2)p eop end %%Page: 3 3 TeXDict begin 3 2 bop 1059 573 a Fp(2.)60 b(Extended)46 b(Dynkin)e(graphs)404 959 y Fl(In)k(this)f(talk)f(w)m(e)h(consider)g Fo(P)1771 976 y Fn(\000)p Fm(;\037;\015)2021 959 y Fl(algebras)f (related)g(to)h(extended)257 1108 y(Dynkin)39 b(graphs)f(and)g(study)h (whether)e(there)i(exist)e Fo(\003)p Fl(-represen)m(tations)257 1257 y(of)i(suc)m(h)g(algebras.)1478 1814 y Fj(s)216 b(s)g(s)1727 1565 y(s)1727 2063 y(s)p 1478 1815 250 4 v 1727 1815 V 1725 1814 4 250 v 1725 2063 V 1517 1599 a Fl(~)1489 1630 y Fg(D)1586 1648 y Fn(4)1063 2909 y Fj(s)299 b(s)g(s)g(s)g(s)1727 2660 y(s)1727 2411 y(s)p 1063 2911 333 4 v 1395 2911 V 1727 2911 V 2059 2911 V 1725 2660 4 250 v 1725 2909 V 1190 2778 a Fl(~)1163 2808 y Fg(E)1250 2826 y Fn(6)731 3685 y Fj(s)g(s)g(s)g(s)g(s)g(s)g(s)1727 3436 y(s)p 731 3687 333 4 v 2391 3687 V 1063 3687 V 1395 3687 V 1727 3687 V 2059 3687 V 1725 3685 4 250 v 1190 3471 a Fl(~)1163 3501 y Fg(E)1250 3519 y Fn(7)1063 4462 y Fj(s)g(s)g(s)g(s)g(s)g(s)g(s)g(s)1727 4213 y(s)p 2723 4463 333 4 v 3055 4463 V 2391 4463 V 1063 4463 V 1395 4463 V 1727 4463 V 2059 4463 V 1725 4462 4 250 v 1190 4247 a Fl(~)1163 4278 y Fg(E)1250 4296 y Fn(8)404 4790 y Fl(In)29 b(what)g(follo)m(ws)e(\006)1284 4808 y Fn(\000)p Fm(;\037)1444 4790 y Fl(denotes)i(the)g(set)g(of)g(those)g Fg(\015)35 b Fl(for)29 b(whic)m(h)f(there)257 4939 y(exist)38 b Fo(\003)p Fl(-represen)m(tation)e(of)i Fo(P)1614 4957 y Fn(\000)p Fm(;\037;\015)1816 4939 y Fl(.)1852 5637 y Fk(3)p eop end %%Page: 4 4 TeXDict begin 4 3 bop 1302 573 a Fp(3.)60 b(Co)l(xeter)47 b(functors)404 959 y Fl(The)53 b(p)s(o)m(w)m(erful)f(to)s(ol)g(to)h(in) m(v)m(estigate)d(algebras)i Fo(P)2710 976 y Fn(\000)p Fm(;\037;\015)2966 959 y Fl(is)i(Co)m(xeter)257 1108 y(functors.)d(There)38 b(are)g(t)m(w)m(o)f(functors)h(of)g(linear)1171 1357 y Fg(S)i Fl(:)33 b(Rep)p Fo(P)1635 1375 y Fn(\000)p Fm(;\037;\015)1870 1357 y Fo(!)g Fl(Rep)p Fo(P)2309 1375 y Fn(\000)p Fm(;\037)2436 1351 y Fb(\003)2474 1375 y Fm(;\015)2549 1357 y Fg(;)474 1623 y(\037)547 1574 y Fd(\003)626 1623 y Fl(=)g(\()p Fg(\015)g Fo(\000)26 b Fg(\013)1084 1574 y Fn(\(1\))1083 1653 y Fm(m)1156 1665 y Ff(1)1198 1623 y Fg(;)20 b(:)g(:)g(:)e(;)i(\015)32 b Fo(\000)27 b Fg(\013)1749 1561 y Fn(\(1\))1748 1655 y(1)1859 1623 y Fl(;)20 b Fg(:)g(:)g(:)e Fl(;)i Fg(\015)32 b Fo(\000)27 b Fg(\013)2410 1574 y Fn(\()p Fm(n)p Fn(\))2409 1653 y Fm(m)2482 1665 y Fe(n)2531 1623 y Fg(;)20 b(:)g(:)g(:)e(;)i (\015)32 b Fo(\000)27 b Fg(\013)3082 1561 y Fn(\()p Fm(n)p Fn(\))3081 1655 y(1)3201 1623 y Fl(\))p 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2510 y Fd(0)1349 2560 y Fl(=)34 b Fg(\013)1549 2510 y Fn(\(1\))1548 2589 y Fm(m)1621 2601 y Ff(1)1689 2560 y Fl(+)27 b Fg(:)20 b(:)g(:)k Fl(+)j Fg(\013)2163 2510 y Fn(\()p Fm(n)p Fn(\))2162 2589 y Fm(m)2235 2601 y Fe(n)2311 2560 y Fo(\000)g Fg(\015)7 b Fl(;)404 2999 y(These)37 b(t)m(w)m(o)f(functors)g(allo)m(w)f(us)j(to) e(construct)g(the)h(irreducible)f(rep-)257 3149 y(resen)m(tations)h(of) h Fo(P)1122 3167 y Fn(\000)p Fm(;\037;\015)1363 3149 y Fl(from)f(the)i(simplest)e(ones.)404 3534 y(In)i(what)f(follo)m(ws)e (\010)1312 3491 y Fn(+)1419 3534 y Fl(denotes)j(the)f(comp)s(osition)e (\010)2783 3491 y Fn(+)2885 3534 y Fl(=)d Fg(S)h Fo(\016)26 b Fg(T)16 b Fl(.)1852 5637 y Fk(4)p eop end %%Page: 5 5 TeXDict begin 5 4 bop 1187 573 a Fp(4.)61 b(In)l(v)-7 b(arian)l(t)46 b(functionals)404 959 y Fl(Let)40 b Fg(!)t Fl(\()p Fg(\037)p Fl(\))h(b)s(e)g(a)f(p)s(ositiv)m(e)f(functional)f(on) i(\000.)57 b(W)-10 b(e)42 b(sa)m(y)e(that)f Fg(!)t Fl(\()p Fg(\037)p Fl(\))i(is)257 1108 y(an)e(in)m(v)-7 b(arian)m(t)36 b(functional)g(if)j(the)f(follo)m(wing)e(conditions)h(holds:)1182 1357 y Fg(S)j Fl(:)33 b(\()p Fg(\037;)20 b(!)t Fl(\()p Fg(\037)p Fl(\)\))31 b Fo(7\000)-19 b(!)32 b Fl(\()p Fg(\037)2196 1308 y Fd(0)2223 1357 y Fg(;)20 b(!)t Fl(\()p Fg(\037)2472 1308 y Fd(0)2499 1357 y Fl(\)\))p Fg(;)1130 1531 y(T)50 b Fl(:)32 b(\()p Fg(\037;)20 b(!)t Fl(\()p Fg(\037)p Fl(\)\))32 b Fo(7\000)-20 b(!)33 b Fl(\()p Fg(\037)2151 1482 y Fd(00)2200 1531 y Fg(;)20 b(!)t Fl(\()p Fg(\037)2449 1482 y Fd(00)2499 1531 y Fl(\)\))p Fg(:)257 1780 y Fl(It)31 b(has)f(b)s(een)h(pro)m(v)m(ed)d(that)i(if)f(\000)i(is) f(an)g(extended)g(Dynkin)g(diagram)e(then)257 1930 y(there)39 b(exists)f(the)g(only)g(in)m(v)-7 b(arian)m(t)36 b(functional:)936 2219 y Fg(!)1028 2233 y Fn(~)1009 2254 y Fm(D)1078 2266 y Ff(4)1119 2219 y Fl(\()p Fg(\037)p Fl(\))c(=)1451 2138 y(1)p 1451 2191 59 5 v 1451 2301 a(2)1519 2219 y(\()p Fg(\013)1640 2157 y Fn(\(1\))1639 2250 y(1)1777 2219 y Fl(+)26 b Fg(\013)1969 2157 y Fn(\(2\))1968 2250 y(1)2106 2219 y Fl(+)h Fg(\013)2299 2157 y Fn(\(3\))2298 2250 y(1)2436 2219 y Fl(+)f Fg(\013)2628 2157 y Fn(\(4\))2627 2250 y(1)2739 2219 y Fl(\))p Fg(;)610 2492 y(!)702 2506 y Fn(~)683 2527 y Fm(E)744 2539 y Ff(6)785 2492 y Fl(\()p Fg(\037)p Fl(\))33 b(=)1117 2411 y(1)p 1117 2465 V 1117 2574 a(3)1186 2492 y(\()p Fg(\013)1307 2430 y Fn(\(1\))1306 2524 y(1)1443 2492 y Fl(+)27 b Fg(\013)1636 2430 y Fn(\(1\))1635 2524 y(2)1773 2492 y Fl(+)f Fg(\013)1965 2430 y Fn(\(2\))1964 2524 y(1)2102 2492 y Fl(+)h Fg(\013)2295 2430 y Fn(\(2\))2294 2524 y(2)2432 2492 y Fl(+)g Fg(\013)2625 2430 y Fn(\(3\))2624 2524 y(1)2762 2492 y Fl(+)f Fg(\013)2954 2430 y Fn(\(3\))2953 2524 y(2)3065 2492 y Fl(\))p Fg(;)416 2765 y(!)508 2779 y Fn(~)489 2800 y Fm(E)550 2812 y Ff(7)591 2765 y Fl(\()p Fg(\037)p Fl(\))33 b(=)923 2684 y(1)p 923 2738 V 923 2847 a(4)992 2765 y(\()p Fg(\013)1113 2703 y Fn(\(1\))1112 2797 y(1)1249 2765 y Fl(+)27 b Fg(\013)1442 2703 y Fn(\(1\))1441 2797 y(2)1579 2765 y Fl(+)f Fg(\013)1771 2703 y Fn(\(1\))1770 2797 y(3)1908 2765 y Fl(+)h Fg(\013)2101 2703 y Fn(\(2\))2100 2797 y(1)2238 2765 y Fl(+)g Fg(\013)2431 2703 y Fn(\(2\))2430 2797 y(2)2568 2765 y Fl(+)f Fg(\013)2760 2703 y Fn(\(2\))2759 2797 y(3)2897 2765 y Fl(+)h(2)p Fg(\013)3149 2703 y Fn(\(3\))3148 2797 y(1)3259 2765 y Fl(\))p Fg(;)257 3038 y(!)349 3052 y Fn(~)330 3074 y Fm(E)391 3086 y Ff(8)433 3038 y Fl(\()p Fg(\037)p Fl(\))33 b(=)765 2957 y(1)p 765 3011 V 765 3120 a(6)833 3038 y(\()p Fg(\013)954 2976 y Fn(\(1\))953 3070 y(1)1091 3038 y Fl(+)26 b Fg(\013)1283 2976 y Fn(\(1\))1282 3070 y(2)1420 3038 y Fl(+)h Fg(\013)1613 2976 y Fn(\(1\))1612 3070 y(3)1750 3038 y Fl(+)g Fg(\013)1943 2976 y Fn(\(1\))1942 3070 y(4)2080 3038 y Fl(+)f Fg(\013)2272 2976 y Fn(\(1\))2271 3070 y(5)2409 3038 y Fl(+)h(2)p Fg(\013)2661 2976 y Fn(\(2\))2660 3070 y(1)2797 3038 y Fl(+)g(2)p Fg(\013)3049 2976 y Fn(\(2\))3048 3070 y(2)3186 3038 y Fl(+)f(3)p Fg(\013)3437 2976 y Fn(\(3\))3436 3070 y(1)3547 3038 y Fl(\))p Fg(:)404 3507 y Fl(In)k(case)g(where)f Fg(\015)40 b Fl(=)33 b Fg(!)1407 3525 y Fn(\000)1463 3507 y Fl(\()p Fg(\037)p Fl(\))c(the)h(algebras)e Fo(P)2380 3528 y Fn(\000)p Fm(;\037;!)2582 3540 y Ff(\000)2627 3528 y Fn(\()p Fm(\037)p Fn(\))2777 3507 y Fl(are)i(PI-algebra)257 3657 y(and)c(their)f(irreducible)e(represen)m(tations)g(are)i(of)h (dimension)e(not)h(greater)257 3806 y(that)38 b(2,3,4)f(and)h(6)h(resp) s(ectiv)m(ely)e(for)1960 3776 y(~)1933 3806 y Fg(D)2030 3824 y Fn(4)2075 3806 y Fl(,)2174 3776 y(~)2147 3806 y Fg(E)2234 3824 y Fn(6)2279 3806 y Fl(,)2378 3776 y(~)2351 3806 y Fg(E)2438 3824 y Fn(7)2483 3806 y Fl(,)i(and)2810 3776 y(~)2782 3806 y Fg(E)2869 3824 y Fn(8)2954 3806 y Fl(diagrams.)404 4105 y(Usign)52 b(these)g(functionals)f(an)h(action) f(of)i(\010)2444 4062 y Fn(+)2565 4105 y Fl(on)f(the)h(pair)e(\()p Fg(\037;)20 b(\015)7 b Fl(\))257 4254 y(functor)38 b(could)g(b)s(e)h (written)e(in)i(the)f(follo)m(wing)d(w)m(a)m(y:)579 4504 y(\(\010)710 4454 y Fn(+)778 4504 y Fl(\))824 4454 y Fm(n)877 4504 y Fl(\()p Fg(\037)p Fl(;)20 b Fg(\015)7 b Fl(\))32 b(=)h(\()p Fg(v)t Fl(\()p Fg(t;)20 b(\037)p Fl(\);)g Fg(w)1823 4521 y Fn(1)1866 4504 y Fl(\()p Fg(t;)g(\037)p Fl(\)\))25 b Fo(\000)i Fg(\025)p Fl(\()p Fg(u)p Fl(\()p Fg(t;)20 b(n)p Fl(\);)g Fg(w)2892 4521 y Fn(2)2935 4504 y Fl(\()p Fg(n)p Fl(\)\))p Fg(;)404 4753 y Fl(where)55 b Fg(\025)63 b Fl(=)f Fg(!)1116 4771 y Fn(\000)1172 4753 y Fl(\()p Fg(\037)p Fl(\))38 b Fo(\000)g Fg(\015)7 b Fl(,)59 b Fg(t)k Fl(=)f([)1986 4706 y Fm(n)p 1967 4725 89 5 v 1967 4794 a(k)2010 4806 y Ff(\000)2065 4753 y Fl(],)d Fg(k)2270 4767 y Fn(~)2251 4788 y Fm(D)2320 4800 y Ff(4)2424 4753 y Fl(=)j(2)p Fg(;)20 b(k)2769 4767 y Fn(~)2750 4788 y Fm(E)2811 4800 y Ff(6)2914 4753 y Fl(=)62 b(6)p Fg(;)20 b(k)3259 4767 y Fn(~)3240 4788 y Fm(E)3301 4800 y Ff(7)3404 4753 y Fl(=)257 4902 y(12)p Fg(;)g(k)508 4916 y Fn(~)489 4937 y Fm(E)550 4949 y Ff(8)624 4902 y Fl(=)33 b(30.)47 b(Notice)28 b(that)h(the)g(v)m(ector)f Fg(v)t Fl(\()p Fg(t;)20 b(n)p Fl(\))28 b(and)h(n)m(um)m(b)s(ers)g Fg(w)3194 4920 y Fn(1)3240 4902 y Fl(\()p Fg(t;)20 b(n)p Fl(\))257 5051 y(dep)s(ends)38 b(on)f Fg(\037)g Fl(and)g(indep)s(enden) m(t)g(on)f Fg(\025)i Fl(and)f(the)g(comp)s(onen)m(ts)e(of)i(the)257 5201 y(v)m(ector)h Fg(u)p Fl(\()p Fg(t;)20 b(n)p Fl(\))37 b(are)h(strictly)f(increasing)f(with)i(n.)1852 5637 y Fk(5)p eop end %%Page: 6 6 TeXDict begin 6 5 bop 1000 573 a Fp(5.)60 b(Description)46 b(of)f(the)g(set)h Fl(\006)2587 587 y Fn(~)2568 608 y Fm(D)2637 620 y Ff(4)2674 608 y Fm(;\037)404 978 y Fl(In)26 b(case)g(where)f(\000)33 b(=)1355 948 y(~)1328 978 y Fg(D)1425 996 y Fn(4)1496 978 y Fl(w)m(e)26 b(ha)m(v)m(e)f(the)g(c)m (haracter)f Fg(\037)2691 992 y Fn(~)2672 1014 y Fm(D)2741 1026 y Ff(4)2815 978 y Fl(=)34 b(\()p Fg(\013)3060 996 y Fn(1)3105 978 y Fl(;)20 b Fg(\013)3232 996 y Fn(2)3278 978 y Fl(;)g Fg(\013)3405 996 y Fn(3)3450 978 y Fl(;)g Fg(\013)3577 996 y Fn(4)3623 978 y Fl(;)g(\))257 1128 y(and)39 b Fo(\003)p Fl(-algebra:)257 1377 y Fo(P)359 1391 y Fn(~)340 1412 y Fm(D)409 1424 y Ff(4)447 1412 y Fm(;\037;\015)630 1377 y Fl(=)33 b Fh(C)p Fo(h)p Fg(p)945 1395 y Fn(1)991 1377 y Fg(;)20 b(p)1103 1395 y Fn(2)1148 1377 y Fg(;)g(p)1260 1395 y Fn(3)1305 1377 y Fg(;)g(p)1417 1395 y Fn(4)1462 1377 y Fo(j)p Fg(p)1554 1395 y Fm(i)1620 1377 y Fl(=)33 b Fg(p)1803 1327 y Fn(2)1803 1406 y Fm(i)1881 1377 y Fl(=)h Fg(p)2065 1327 y Fd(\003)2065 1406 y Fm(i)2110 1377 y Fg(;)20 b(\013)2237 1395 y Fn(1)2283 1377 y Fg(p)2342 1395 y Fn(1)2387 1377 y Fl(+)p Fg(\013)2552 1395 y Fn(2)2598 1377 y Fg(p)2657 1395 y Fn(2)2703 1377 y Fl(+)p Fg(\013)2868 1395 y Fn(3)2914 1377 y Fg(p)2973 1395 y Fn(3)3018 1377 y Fl(+)p Fg(\013)3183 1395 y Fn(4)3229 1377 y Fg(p)3288 1395 y Fn(4)3367 1377 y Fl(=)33 b Fg(\015)7 b(e)p Fo(i)p Fg(:)404 1626 y Fl(W)-10 b(e)45 b(assume)f(that)f(all)h(comp)s(onen)m (ts)f(of)h(the)g(c)m(haracter)e(satisfy)i(the)257 1775 y(condition)39 b Fg(\013)847 1793 y Fm(i)916 1775 y Fg(<)1053 1728 y Fm(\013)p 1053 1748 54 5 v 1059 1817 a Fn(2)1117 1775 y Fl(,)i(where)e Fg(\013)f Fl(=)e Fg(\013)1843 1793 y Fn(1)1917 1775 y Fl(+)28 b Fg(\013)2110 1793 y Fn(2)2184 1775 y Fl(+)f Fg(\013)2376 1793 y Fn(3)2450 1775 y Fl(+)h Fg(\013)2643 1793 y Fn(4)2689 1775 y Fl(.)57 b(One)41 b(can)f(sho)m(w)257 1925 y(that)48 b(in)h(case)g(one)g(comp)s(onen)m (ts)f(do)s(esn't)g(satisfy)g(this)h(condition)e(w)m(e)257 2074 y(get)38 b(algebra)f(with)h(the)g(relation:)1226 2323 y Fg(\013)1301 2274 y Fd(0)1300 2353 y Fn(1)1346 2323 y Fg(p)1405 2341 y Fn(1)1477 2323 y Fl(+)27 b Fg(\013)1670 2274 y Fd(0)1669 2353 y Fn(2)1715 2323 y Fg(p)1774 2341 y Fn(2)1846 2323 y Fl(+)g Fg(\013)2039 2274 y Fd(0)2038 2353 y Fn(3)2084 2323 y Fg(p)2143 2341 y Fn(3)2221 2323 y Fl(=)34 b Fg(\015)2414 2274 y Fd(0)2440 2323 y Fg(e;)257 2572 y Fl(where)39 b(the)f(answ)m(er)g(in)g(kno)m(wn.)404 2722 y(Using)g(considered)g(tec)m(hnique)f(w)m(e)i(ha)m(v)m(e)f (describ)s(ed)g(the)h(set)g(\006)3281 2736 y Fn(~)3262 2757 y Fm(D)3331 2769 y Ff(4)3367 2757 y Fm(;\037)257 2954 y Fp(Lemma)54 b(1.)45 b Fa(The)j(set)f Fl(\006)1429 2968 y Fn(~)1410 2990 y Fm(D)1479 3002 y Ff(4)1516 2990 y Fm(;\037)1643 2954 y Fa(c)-6 b(ontains)47 b(the)h(in\014nity)e (series)i Fl(\006)3148 2972 y Fd(1)3283 2954 y Fa(with)257 3104 y(limit)h(p)-6 b(oint)856 3057 y Fm(\013)p 856 3076 V 862 3145 a Fn(2)969 3104 y Fa(and)48 b(the)h(\014nite)f(series)h Fl(\006)2137 3122 y Fn(0)2182 3104 y Fa(.)76 b(This)48 b(two)h(series)g(ar)-6 b(e)49 b(de-)257 3253 y(scrib)-6 b(e)g(d)41 b(by)h(the)f(fol)6 b(lowing)40 b(rule:)357 3486 y(1.)48 b(when)41 b Fg(\013)874 3504 y Fn(2)947 3486 y Fl(+)26 b Fg(\013)1138 3504 y Fn(3)1218 3486 y Fg(>)33 b(\013)1416 3504 y Fn(1)1489 3486 y Fl(+)26 b Fg(\013)1680 3504 y Fn(4)1768 3486 y Fa(then)41 b Fl(\006)2113 3504 y Fd(1)2233 3486 y Fl(=)2357 3389 y Fc(\010)2437 3439 y Fm(\013)p 2437 3458 V 2443 3527 a Fn(2)2527 3486 y Fo(\000)2657 3436 y Fm(\013)2710 3448 y Ff(1)p 2657 3458 92 5 v 2657 3527 a Fn(2)p Fm(n)2758 3486 y Fo(j)p Fg(n)33 b Fo(2)g Fh(N)3093 3389 y Fc(\011)3205 3486 y Fa(and)501 3673 y Fl(\006)586 3691 y Fn(0)665 3673 y Fl(=)789 3541 y Fc(n)879 3626 y Fm(\013)p 879 3646 54 5 v 885 3714 a Fn(2)969 3673 y Fo(\000)1125 3624 y Fm(\013)p Fd(\000)p Fn(2)p Fm(\013)1338 3636 y Ff(4)p 1098 3646 304 5 v 1098 3714 a Fn(2\(2)p Fm(n)p Fd(\000)p Fn(1\))1412 3673 y Fo(j)p Fg(n)g(<)1939 3626 y Fn(1)p 1682 3646 556 5 v 1682 3714 a Fm(\013)1735 3726 y Ff(2)1772 3714 y Fn(+)p Fm(\013)1890 3726 y Ff(3)1927 3714 y Fd(\000)p Fm(\013)2045 3726 y Ff(1)2082 3714 y Fd(\000)p Fm(\013)2200 3726 y Ff(4)2247 3673 y Fg(;)20 b(n)33 b Fo(2)g Fh(N)2602 3541 y Fc(o)357 3980 y Fa(2.)48 b(when)h Fg(\013)882 3998 y Fn(2)960 3980 y Fl(+)32 b Fg(\013)1157 3998 y Fn(3)1250 3980 y Fg(<)47 b(\013)1462 3998 y Fn(1)1540 3980 y Fl(+)33 b Fg(\013)1738 3998 y Fn(4)1833 3980 y Fa(then)49 b Fl(\006)2186 3998 y Fd(1)2319 3980 y Fl(=)2457 3847 y Fc(n)2547 3933 y Fm(\013)p 2547 3952 54 5 v 2553 4021 a Fn(2)2637 3980 y Fo(\000)2793 3930 y Fm(\013)p Fd(\000)p Fn(2)p Fm(\013)3006 3942 y Ff(4)p 2767 3952 304 5 v 2767 4021 a Fn(2\(2)p Fm(n)p Fd(\000)p Fn(1\))3080 3980 y Fo(j)p Fg(n)33 b Fo(2)g Fh(N)3415 3847 y Fc(o)501 4149 y Fa(and)501 4298 y Fl(\006)586 4316 y Fn(0)665 4298 y Fl(=)789 4166 y Fc(n)879 4251 y Fm(\013)p 879 4271 54 5 v 885 4339 a Fn(2)969 4298 y Fo(\000)1099 4249 y Fm(\013)1152 4261 y Ff(1)p 1098 4271 92 5 v 1098 4339 a Fn(2)p Fm(n)1199 4298 y Fo(j)p Fg(n)h(<)1727 4251 y Fn(1)p 1470 4271 556 5 v 1470 4339 a Fm(\013)1523 4351 y Ff(1)1560 4339 y Fn(+)p Fm(\013)1678 4351 y Ff(4)1715 4339 y Fd(\000)p Fm(\013)1833 4351 y Ff(2)1870 4339 y Fd(\000)p Fm(\013)1988 4351 y Ff(3)2035 4298 y Fg(;)20 b(n)32 b Fo(2)h Fh(N)2389 4166 y Fc(o)357 4569 y Fa(3.)48 b(when)g Fg(\013)881 4587 y Fn(2)960 4569 y Fl(+)32 b Fg(\013)1157 4587 y Fn(3)1250 4569 y Fl(=)47 b Fg(\013)1462 4587 y Fn(1)1540 4569 y Fl(+)32 b Fg(\013)1737 4587 y Fn(4)1832 4569 y Fa(then)48 b Fl(\006)2184 4587 y Fd(1)2318 4569 y Fl(=)2456 4472 y Fc(\010)2536 4522 y Fm(\013)p 2536 4541 54 5 v 2542 4610 a Fn(2)2626 4569 y Fo(\000)2755 4519 y Fm(\013)2808 4531 y Ff(1)p 2755 4541 91 5 v 2775 4610 a Fm(n)2855 4569 y Fo(j)p Fg(n)34 b Fo(2)f Fh(N)3191 4472 y Fc(\011)3310 4569 y Fa(and)501 4718 y Fl(\006)586 4736 y Fn(0)665 4718 y Fl(=)g Fh(?)p Fa(.)1852 5637 y Fk(6)p eop end %%Page: 7 7 TeXDict begin 7 6 bop 257 573 a Fp(Theorem)45 b(1.)257 822 y Fl(\006)361 836 y Fn(~)342 857 y Fm(D)411 869 y Ff(4)448 857 y Fm(;\037)527 822 y Fo(\\)p Fl([0;)20 b Fg(\013)q(=)p Fl(2\))30 b(=)k(\006)1231 840 y Fd(1)1317 822 y Fo([)p Fl(\006)1482 840 y Fn(0)1527 822 y Fo([)p Fl(\006)1692 840 y Fn(1)1737 822 y Fo([)p Fl(\006)1902 773 y Fm(i)1902 851 y Fn(2)1947 822 y Fo([)p Fl(\006)2112 840 y Fn(3)2157 822 y Fo([)p Fl(\006)2322 840 y Fn(4)2367 822 y Fo([)p Fl(\006)2532 765 y Fm(j)2532 853 y Fn(5)2577 822 y Fg(;)139 b(i)33 b Fl(=)g(2)p Fg(;)20 b Fl(3)p Fg(;)g Fl(4)p Fg(;)137 b(j)40 b Fl(=)33 b(1)p Fg(;)20 b Fl(2)p Fg(;)g Fl(3)p Fg(;)257 1119 y Fa(wher)-6 b(e)42 b Fl(\006)673 1137 y Fn(1)751 1119 y Fl(=)875 986 y Fc(n)965 1072 y Fm(\013)p 965 1091 54 5 v 971 1160 a Fn(2)1055 1119 y Fo(\000)1309 1072 y Fm(\013)p 1184 1091 304 5 v 1184 1160 a Fn(2\(4)p Fm(n)p Fd(\000)p Fn(1\))1498 1119 y Fo(j)e Fg(n)33 b(<)1888 1069 y Fm(\013)1941 1081 y Ff(4)p 1808 1091 250 5 v 1808 1160 a Fn(4)p Fm(\013)1903 1172 y Ff(4)1940 1160 y Fd(\000)p Fm(\013)2068 1119 y Fg(;)20 b(n)33 b(<)2379 1069 y Fm(\013)p Fd(\000)p Fm(\013)2550 1081 y Ff(1)p 2358 1091 V 2358 1160 a Fm(\013)p Fd(\000)p Fn(4)p Fm(\013)2571 1172 y Ff(1)2618 1119 y Fg(;)20 b(n)32 b Fo(2)h Fh(N)2972 986 y Fc(o)3072 1119 y Fg(;)257 1442 y Fl(\006)342 1392 y Fm(i)342 1471 y Fn(2)421 1442 y Fl(=)545 1309 y Fc(n)635 1361 y Fg(\013)p 635 1414 76 5 v 643 1524 a Fl(2)746 1442 y Fo(\000)887 1361 y Fg(\013)961 1379 y Fm(i)p 876 1414 129 5 v 876 1524 a Fl(2)p Fg(n)1014 1442 y Fo(j)p Fg(i)h Fl(=)f(2)p Fg(;)20 b Fl(3)p Fg(;)g Fl(4;)27 b Fg(n)33 b(<)2126 1361 y(\013)2200 1379 y Fm(i)p 1825 1414 710 5 v 1825 1524 a Fl(2)p Fg(\013)1958 1542 y Fm(i)2017 1524 y Fl(+)27 b(2)p Fg(\013)2268 1542 y Fn(4)2340 1524 y Fo(\000)g Fg(\013)2545 1442 y(;)20 b(n)33 b(<)2968 1361 y(\013)3042 1379 y Fm(i)p 2835 1414 374 5 v 2835 1524 a Fg(\013)2909 1542 y Fm(i)2968 1524 y Fo(\000)27 b Fg(\013)3162 1542 y Fn(1)1618 1748 y Fg(n)33 b(<)1995 1667 y(\013)2069 1685 y Fm(i)p 1855 1721 388 5 v 1855 1830 a Fl(4)p Fg(\013)1988 1848 y Fm(i)2047 1830 y Fo(\000)27 b Fg(\013)2252 1748 y(;)20 b(n)33 b Fo(2)f Fh(N)2606 1580 y Fc(\033)2716 1748 y Fg(;)139 b(i)34 b Fl(=)f(2)p Fg(;)20 b Fl(3)p Fg(;)g Fl(4)p Fg(;)425 2068 y Fl(\006)510 2086 y Fn(3)589 2068 y Fl(=)713 1900 y Fc(\032)813 1988 y Fg(\013)p 813 2041 76 5 v 821 2150 a Fl(2)924 2068 y Fo(\000)1094 1988 y Fg(\013)28 b Fo(\000)f Fl(2)p Fg(\013)1449 2006 y Fn(1)p 1054 2041 481 5 v 1054 2150 a Fl(2\(2)p Fg(n)e Fl(+)i(1\))1545 2068 y Fo(j)40 b Fg(n)33 b(<)1884 1988 y(\013)28 b Fo(\000)f Fg(\013)2180 2006 y Fn(1)p 1855 2041 400 5 v 1855 2150 a Fg(\013)h Fo(\000)e Fl(4)p Fg(\013)2209 2168 y Fn(1)2265 2068 y Fg(;)20 b(n)32 b(<)2630 1988 y(\013)2704 2006 y Fn(2)2777 1988 y Fl(+)27 b Fg(\013)2969 2006 y Fn(3)p 2555 2041 536 5 v 2555 2150 a Fl(2\()p Fg(\013)2734 2168 y Fn(4)2805 2150 y Fo(\000)g Fg(\013)2999 2168 y Fn(1)3045 2150 y Fl(\))3101 2068 y Fg(;)20 b(n)32 b Fo(2)h Fh(N)3455 1900 y Fc(\033)3565 2068 y Fg(;)425 2389 y Fl(\006)510 2407 y Fn(4)589 2389 y Fl(=)713 2220 y Fc(\032)813 2308 y Fg(\013)p 813 2361 76 5 v 821 2471 a Fl(2)924 2389 y Fo(\000)1257 2308 y Fg(\013)p 1054 2361 481 5 v 1054 2471 a Fl(2\(4)p Fg(n)25 b Fl(+)i(1\))1545 2389 y Fo(j)40 b Fg(n)33 b(<)1884 2308 y(\013)28 b Fo(\000)f Fg(\013)2180 2326 y Fn(4)p 1855 2361 400 5 v 1855 2471 a Fl(4)p Fg(\013)1988 2489 y Fn(4)2060 2471 y Fo(\000)g Fg(\013)2265 2389 y(;)20 b(n)32 b(<)2695 2308 y(\013)2769 2326 y Fn(1)p 2555 2361 V 2555 2471 a Fg(\013)27 b Fo(\000)g Fl(4)p Fg(\013)2909 2489 y Fn(1)2965 2389 y Fg(;)20 b(n)32 b Fo(2)h Fh(N)3319 2220 y Fc(\033)3429 2389 y Fg(;)257 3170 y Fl(\006)342 3121 y Fm(i)342 3200 y Fn(5)421 3170 y Fl(=)545 3002 y Fc(\032)645 3089 y Fg(\013)p 645 3143 76 5 v 653 3252 a Fl(2)756 3170 y Fo(\000)933 3089 y Fg(\013)28 b Fo(\000)e Fl(2)p Fg(\013)1287 3107 y Fm(i)p 886 3143 481 5 v 886 3252 a Fl(2\(2)p Fg(n)f Fl(+)i(1\))1377 3170 y Fo(j)10 b Fg(n)33 b(<)1953 3089 y(\013)2027 3107 y Fn(1)p 1657 3143 712 5 v 1657 3252 a Fg(\013)28 b Fo(\000)e Fl(2)p Fg(\013)2011 3270 y Fm(i)2071 3252 y Fo(\000)g Fl(2)p Fg(\013)2323 3270 y Fn(1)2379 3170 y Fg(;)20 b(n)32 b(<)2809 3089 y(\013)2883 3107 y Fm(i)p 2669 3143 388 5 v 2669 3252 a Fg(\013)27 b Fo(\000)g Fl(4)p Fg(\013)3023 3270 y Fm(i)3066 3170 y Fg(;)1450 3490 y(n)33 b(<)1687 3410 y(\013)28 b Fo(\000)e Fg(\013)1982 3428 y Fn(4)2055 3410 y Fo(\000)h Fg(\013)2249 3428 y Fm(i)p 1687 3463 595 5 v 1723 3573 a Fl(2\()p Fg(\013)1902 3590 y Fn(4)1974 3573 y Fo(\000)f Fg(\013)2167 3590 y Fm(i)2200 3573 y Fl(\))2292 3490 y Fg(;)20 b(n)32 b Fo(2)h Fh(N)27 b Fo([)f(f)p Fl(0)p Fo(g)2958 3322 y Fc(\033)3067 3490 y Fg(;)139 b(i)33 b Fl(=)g(1)p Fg(;)20 b Fl(2)p Fg(;)g Fl(3)p Fg(:)1852 5637 y Fk(7)p eop end %%Page: 8 8 TeXDict begin 8 7 bop 1123 573 a Fp(6.)60 b(In\014nit)l(y)45 b(of)g(the)h(sets)f Fl(\006)2499 591 y Fn(\000)p Fm(;\037)404 959 y Fl(When)39 b(sets)g(\006)1059 976 y Fn(\000)p Fm(;\037)1229 959 y Fl(are)f(in\014nite?)404 1226 y(One)53 b(can)g(sho)m(w)g(that)f (if)h(at)f(least)g(one)h(comp)s(onen)m(t)f(of)h(c)m(haracter)257 1376 y(satis\014es)e(one)g(of)g(the)g(inequalities)e Fg(\037)1989 1393 y Fm(i)2076 1376 y Fo(\025)55 b Fg(!)2297 1393 y Fn(\000)2353 1376 y Fl(\()p Fg(\037)p Fl(\))50 b(or)75 b(~)-83 b Fg(\037)2797 1393 y Fm(i)2884 1376 y Fo(\025)55 b Fg(!)3105 1393 y Fn(\000)3161 1376 y Fl(\()p Fg(S)7 b Fl(\()p Fg(\037)p Fl(\)\))257 1525 y(then)52 b(corresp)s(onding)d(pro)7 b(jector)49 b(is)i(equal)f(to)h(0)g(or)g(to) g Fg(I)9 b Fl(,)54 b(hence)e(the)257 1674 y(sets)39 b(\006)571 1692 y Fn(\000)p Fm(;\037)741 1674 y Fl(are)f(\014nite.)404 1942 y(W)-10 b(e)43 b(pro)m(v)m(e)d(that)h(if)h(all)f(comp)s(onen)m(ts) g(of)g(the)h(c)m(haracter)e(satisfy)h(the)257 2091 y(follo)m(wing)36 b(conditions:)1582 2241 y Fg(\037)1655 2259 y Fm(i)1721 2241 y Fg(<)d(!)1918 2259 y Fn(\000)1974 2241 y Fl(\()p Fg(\037)p Fl(\);)1605 2444 y(~)-82 b Fg(\037)1655 2462 y Fm(i)1721 2444 y Fg(<)33 b(!)1918 2462 y Fn(\000)1974 2444 y Fl(\()14 b(~)-73 b Fg(\037)p Fl(\);)257 2648 y(then)33 b(the)f(sets)g(\006)1020 2666 y Fn(\000)p Fm(;\037)1183 2648 y Fl(are)g(in\014nite.)48 b(T)-10 b(o)32 b(sho)m(w)g(this)g(w)m(e) g(build)f(the)i(in\014nite)257 2797 y(series)39 b(of)f Fg(\015)45 b Fl(for)38 b(eac)m(h)h(there)f(exist)g(represen)m(tation)e (of)i Fo(P)2810 2815 y Fn(\000)p Fm(;\037;\015)3012 2797 y Fl(.)404 3065 y(Let's)g(see)h(ho)m(w)f(it)g(w)m(orks)g(when)g(\000)c (=)2138 3034 y(~)2111 3065 y Fg(E)2198 3083 y Fn(6)2243 3065 y Fl(.)361 3322 y(1.)48 b(Consider)35 b(the)i(sets)f Fg(A)1501 3340 y Fm(\037)1553 3352 y Fe(i)1618 3322 y Fl(=)d Fo(f)p Fg(v)1859 3340 y Fm(i)1891 3322 y Fl(\()p Fg(j;)20 b(\037)p Fl(\))p Fo(j)p Fg(j)40 b Fl(=)34 b(1)p Fg(;)20 b(::;)g(k)2714 3336 y Fn(~)2695 3357 y Fm(E)2756 3369 y Ff(6)2828 3322 y Fl(=)33 b(6)p Fo(g)j Fl(and)h(the)501 3471 y(set)i Fg(A)33 b Fl(=)g Fo([)p Fg(A)1097 3489 y Fm(\037)1149 3501 y Fe(i)1180 3471 y Fl(;)361 3704 y(2.)48 b(Put)38 b Fg(a)c Fl(=)f(min)19 b Fg(A)p Fl(;)361 3936 y(3.)48 b(Let)39 b Fg(p)p Fl(,)f Fg(s)h Fl(b)s(e)h(suc)m(h)f(indexes)f (that)g Fg(v)2083 3954 y Fm(p)2129 3936 y Fl(\()p Fg(s;)20 b(\037)p Fl(\))32 b(=)h Fg(a)257 4194 y Fp(Theorem)54 b(2.)45 b Fa(A)m(lgebr)-6 b(a)47 b Fo(P)1513 4208 y Fn(~)1494 4229 y Fm(E)1555 4241 y Ff(6)1593 4229 y Fm(;\037;\015)1734 4241 y Fe(n)1783 4194 y Fa(,)j(wher)-6 b(e)48 b Fg(\015)2267 4212 y Fm(n)2366 4194 y Fl(=)d Fg(!)2594 4208 y Fn(~)2575 4229 y Fm(E)2636 4241 y Ff(6)2677 4194 y Fl(\()p Fg(\037)p Fl(\))31 b Fo(\000)3117 4147 y Fm(a)p 3007 4166 263 5 v 3007 4235 a(u)3055 4247 y Fe(p)3093 4235 y Fn(\()p Fm(s;n)p Fn(\))3328 4194 y Fa(has)257 4343 y(the)42 b(r)-6 b(epr)g(esentation)40 b(for)i(every)f(natur)-6 b(al)41 b Fg(n)33 b(>)g Fl(2)p Fa(.)404 4576 y("Pr)-6 b(o)g(of")45 b Fl(V)-10 b(erify)45 b(that)f(it)h(is)h(p)s(ossible)f(to)g(use)h(\010) 2593 4532 y Fn(+)2707 4576 y Fl(functor)e(\()p Fg(n)31 b Fo(\000)g Fl(2\))257 4725 y(times.)51 b(Sho)m(w)38 b(that)f(w)m(e)i(obtain)e(the)h(algebra)f(with)h(the)g(relation:)660 4974 y Fg(\013)735 4925 y Fd(0)734 5004 y Fn(1)780 4974 y Fg(p)839 4992 y Fn(1)911 4974 y Fl(+)27 b Fg(\013)1104 4925 y Fd(0)1103 5004 y Fn(2)1149 4974 y Fg(p)1208 4992 y Fn(2)1280 4974 y Fl(+)f Fg(\013)1472 4925 y Fd(0)1471 5004 y Fn(3)1518 4974 y Fg(p)1577 4992 y Fn(3)1649 4974 y Fl(+)g Fg(\013)1841 4925 y Fd(0)1840 5004 y Fn(4)1886 4974 y Fg(p)1945 4992 y Fn(4)2017 4974 y Fl(+)h Fg(\013)2210 4925 y Fd(0)2209 5004 y Fn(5)2255 4974 y Fg(p)2314 4992 y Fn(5)2386 4974 y Fl(+)g Fg(\013)2579 4925 y Fd(0)2578 5004 y Fn(6)2624 4974 y Fg(p)2683 4992 y Fn(6)2761 4974 y Fl(=)34 b Fg(\013)2961 4925 y Fd(0)2960 5004 y Fn(6)3006 4974 y Fg(e:)404 5223 y Fl(This)61 b(pro)s(cedure)g(could)h(b)s(e)g (applied)f(for)g(all)g(extended)h(Dynkin)257 5373 y(graphs,)38 b(hence)h(w)m(e)f(pro)m(v)m(e)g(the)g(follo)m(wing)d(theorem:)1852 5637 y Fk(8)p eop end %%Page: 9 9 TeXDict begin 9 8 bop 257 573 a Fp(Theorem)60 b(3.)47 b Fa(L)-6 b(et)53 b Fl(\000)h Fa(b)-6 b(e)53 b(an)f(extende)-6 b(d)52 b(Dynkin)g(diagr)-6 b(am.)87 b(The)53 b(set)257 722 y Fl(\006)342 740 y Fn(\000)p Fm(;\037)508 722 y Fa(is)35 b(in\014nite)e(i\013)i(e)-6 b(ach)34 b(c)-6 b(omp)g(onent)33 b(of)i(char)-6 b(acter)34 b(satis\014es)g(two)g(c)-6 b(on-)257 872 y(ditions:)53 b Fg(\037)764 890 y Fm(i)830 872 y Fg(<)33 b(!)1027 890 y Fn(\000)1083 872 y Fl(\()p Fg(\037)p Fl(\))41 b Fa(and)65 b Fl(~)-82 b Fg(\037)1590 890 y Fm(i)1656 872 y Fg(<)33 b(!)1853 890 y Fn(\000)1909 872 y Fl(\()14 b(~)-73 b Fg(\037)p Fl(\))p Fa(.)257 1340 y Fp(Corollary)67 b(1.)48 b Fa(\(R)-6 b(epr)g(esentation)55 b(on)g(the)h(hyp)-6 b(erplane)54 b Fg(\015)66 b Fl(=)60 b Fg(!)3227 1358 y Fn(\000)3283 1340 y Fl(\()p Fg(\037)p Fl(\))p Fa(\))257 1490 y(L)-6 b(et)50 b Fl(\000)g Fa(b)-6 b(e)49 b(an)h(extende)-6 b(d)48 b(Dynkin)h(diagr)-6 b(am,)50 b(and)f Fg(\037)h Fa(b)-6 b(e)50 b(the)f(char)-6 b(acter)257 1639 y(on)44 b Fl(\000)h Fa(such)e(that)h(the)g(c)-6 b(onditions)42 b(of)i(Th.2)f(ar)-6 b(e)45 b(satis\014e)-6 b(d.)59 b(Then)44 b(ther)-6 b(e)257 1789 y(exist)41 b(a)h(r)-6 b(epr)g(esentation)40 b(of)i(algebr)-6 b(a)41 b Fo(P)2010 1810 y Fn(\000)p Fm(;\037;!)2212 1822 y Ff(\000)2257 1810 y Fn(\()p Fm(\037)p Fn(\))404 2021 y Fa("Pr)-6 b(o)g(of")51 b Fl(According)f(to)h(Sh)m(ulman's)f(theorem)g(the)h(sets)h(\006)3157 2039 y Fn(\000)p Fm(;\037)3339 2021 y Fl(are)257 2171 y(closed.)69 b(Since)45 b(the)g(conditions)e(of)h(Th.)69 b(4)45 b(are)f(satis\014ed)g(there)g(is)h(the)257 2320 y(series)51 b(in)f(\006)816 2338 y Fn(\000)p Fm(;\037)998 2320 y Fl(with)f(the)h(limit)f(p)s(oin)m(t)g Fg(!)2171 2338 y Fn(\000)2227 2320 y Fl(\()p Fg(\037)p Fl(\).)87 b(Hence)51 b(the)f(set)h(\006)3365 2338 y Fn(\000)p Fm(;\037)257 2470 y Fl(con)m(tains)38 b(p)s(oin)m(t)f Fg(!)1095 2487 y Fn(\000)1151 2470 y Fl(\()p Fg(\037)p Fl(\).)1852 5637 y Fk(9)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF