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cleartomark
%%EndFont 
%%BeginFont: CMTI10
%!PS-AdobeFont-1.1: CMTI10 1.00B
%%CreationDate: 1992 Feb 19 19:56:16
% 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 (CMTI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMTI10 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{-163 -250 1146 969}readonly def
/UniqueID 5000828 def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: CMBX10
%!PS-AdobeFont-1.1: CMBX10 1.00B
%%CreationDate: 1992 Feb 19 19:54:06
% 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 (CMBX10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Bold) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /CMBX10 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{-301 -250 1164 946}readonly def
/UniqueID 5000768 def
currentdict end
currentfile eexec
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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: 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
D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE
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532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470
B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B
986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE
D919C2DDD26BDC0D99398B9F4D03D77639DF1232A4D6233A9CAF69B151DFD33F
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B078D20B4B8A6D7F0300CF694E6956FF9C29C84FCC5C9E8890AA56B1BC60E868
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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 12 /vextendsingle put
dup 18 /parenleftbigg put
dup 19 /parenrightbigg put
dup 48 /parenlefttp put
dup 49 /parenrighttp put
dup 64 /parenleftbt put
dup 65 /parenrightbt put
dup 66 /parenleftex put
dup 67 /parenrightex put
dup 68 /angbracketleftBig put
dup 69 /angbracketrightBig put
dup 112 /radicalbig put
readonly def
/FontBBox{-24 -2960 1454 772}readonly def
/UniqueID 5000774 def
currentdict end
currentfile eexec
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2DF2FC004C8F24C045FF0D3E79C108450DCA1E36880D8B4623D4EB76AFEF84F5
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45C71007813AF5F5F0229BB237C7B9E3C86B65547C03156823F5C3E22CD6B52A
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cleartomark
%%EndFont 
%%BeginFont: MSBM10
%!PS-AdobeFont-1.1: MSBM10 2.1
%%CreationDate: 1993 Sep 17 11:10:37
% Math Symbol fonts were designed by the American Mathematical Society.
% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
/FontInfo 7 dict dup begin
/version (2.1) readonly def
/Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def
/FullName (MSBM10) readonly def
/FamilyName (Euler) readonly def
/Weight (Medium) readonly def
/ItalicAngle 0 def
/isFixedPitch false def
end readonly def
/FontName /MSBM10 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 67 /C put
readonly def
/FontBBox{-55 -420 2343 920}readonly def
/UniqueID 5031982 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
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/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: 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
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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. All Rights Reserved) readonly def
/FullName (CMMI10) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI10 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{-32 -250 1048 750}readonly def
/UniqueID 5087385 def
currentdict end
currentfile eexec
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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
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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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cleartomark
%%EndFont 
%%BeginFont: CMMI12
%!PS-AdobeFont-1.1: CMMI12 1.100
%%CreationDate: 1996 Jul 27 08:57:55
% 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 (CMMI12) readonly def
/FamilyName (Computer Modern) readonly def
/Weight (Medium) readonly def
/ItalicAngle -14.04 def
/isFixedPitch false def
end readonly def
/FontName /CMMI12 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{-30 -250 1026 750}readonly def
/UniqueID 5087386 def
currentdict end
currentfile eexec
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2291 y(~)2222 2312 y Fj(E)2283 2324 y Fi(6)2321 2312
y Fk(\))h(w)n(ere)e(discussed)i(in)f([3].)639 2412 y(W)-7
b(e)28 b(consider)f(represen)n(tations)e(of)j(the)g Fh(\003)p
Fk(-algebra)602 2615 y Fg(C)662 2523 y Ff(D)712 2615
y Fj(p)754 2627 y Fi(1)792 2615 y Fj(;)14 b(p)871 2627
y Fi(2)907 2615 y Fj(;)g(p)986 2627 y Fi(3)1023 2615
y Fj(;)g(q)1097 2627 y Fi(1)1135 2615 y Fj(;)g(q)1209
2627 y Fi(2)1246 2615 y Fj(;)g(q)1320 2627 y Fi(3)1357
2615 y Fj(;)g(r)1457 2520 y Ff(\014)1457 2569 y(\014)1457
2619 y(\014)1507 2615 y Fj(p)1549 2627 y Fe(j)1584 2615
y Fj(p)1626 2627 y Fe(k)1690 2615 y Fk(=)22 b Fj(\016)1814
2627 y Fe(j)s(k)1886 2615 y Fj(p)1928 2627 y Fe(j)1986
2615 y Fk(=)g Fj(p)2115 2581 y Fd(\003)2115 2636 y Fe(j)2153
2615 y Fj(;)14 b(q)2227 2627 y Fe(j)2262 2615 y Fj(q)2299
2627 y Fe(k)2363 2615 y Fk(=)23 b Fj(\016)2488 2627 y
Fe(j)s(k)2560 2615 y Fj(q)2597 2627 y Fe(j)2655 2615
y Fk(=)f Fj(q)2782 2581 y Fd(\003)2779 2636 y Fe(j)2821
2615 y Fj(;)14 b(r)2897 2581 y Fi(2)2957 2615 y Fk(=)23
b Fj(r)3084 2581 y Fd(\003)3146 2615 y Fk(=)g Fj(r)n(;)1168
2798 y(p)1210 2810 y Fi(1)1265 2798 y Fk(+)18 b(2)p Fj(p)1432
2810 y Fi(2)1487 2798 y Fk(+)g(3)p Fj(p)1654 2810 y Fi(3)1709
2798 y Fk(+)g Fj(q)1829 2810 y Fi(1)1885 2798 y Fk(+)g(2)p
Fj(q)2047 2810 y Fi(2)2103 2798 y Fk(+)g(3)p Fj(q)2265
2810 y Fi(3)2320 2798 y Fk(+)g(2)p Fj(r)25 b Fk(=)e(4)p
Fj(e)2676 2706 y Ff(E)515 3001 y Fk(or)34 b(equiv)-5
b(alen)n(tly)e(,)37 b(pairs)d(of)h(self-adjoin)n(t)g(op)r(erators)e
Fj(A)p Fk(,)k Fj(B)i Fk(ha)n(ving)34 b(their)i(sp)r(ectrum)f(in)515
3100 y(the)29 b(set)f Fh(f\006)p Fk(1)p Fj(=)p Fk(2)p
Fj(;)14 b Fh(\006)p Fk(3)p Fj(=)p Fk(2)p Fh(g)24 b Fk(suc)n(h)k(that)g
(\()p Fj(A)20 b Fk(+)e Fj(B)t Fk(\))1980 3070 y Fi(2)2043
3100 y Fk(=)24 b Fj(I)7 b Fk(.)39 b(According)27 b(to)i([1)o(])g(to)f
(this)h(algebra)515 3200 y(there)e(corresp)r(onds)f(the)1345
3179 y(~)1326 3200 y Fj(E)1387 3212 y Fi(7)1452 3200
y Fk(extended)i(Dynkin)g(diagram.)515 3366 y Fc(Theorem)j(1.)41
b Fb(The)31 b(fol)t(lowing)h(p)l(airs)f(ar)l(e)f(r)l(epr)l(esentations)
g(of)g(the)2733 3345 y Fk(~)2714 3366 y Fj(E)2775 3378
y Fi(7)2842 3366 y Fb(algebr)l(a)736 3713 y Fj(A)23 b
Fk(=)944 3657 y(1)p 919 3694 91 4 v 919 3770 a(8)p Fj(\036)1034
3496 y Ff(0)1034 3642 y(B)1034 3692 y(B)1034 3745 y(@)1157
3553 y Fh(\000)p Fk(16)17 b Fh(\000)h Fj(\014)326 b Fk(2)p
Fj(\015)2140 3480 y Ff(p)p 2223 3480 319 4 v 73 x Fk(4)p
Fj(\036)2314 3529 y Fi(4)2369 3553 y Fh(\000)18 b Fj(\014)2503
3529 y Fi(2)2836 3553 y Fk(0)1263 3662 y(2)p Fj(\015)358
b Fk(16)17 b(+)h Fj(\014)383 b Fk(0)262 b Fh(\000)2689
3589 y Ff(p)p 2772 3589 V 73 x Fk(4)p Fj(\036)2863 3638
y Fi(4)2918 3662 y Fh(\000)18 b Fj(\014)3052 3638 y Fi(2)1106
3699 y Ff(p)p 1189 3699 V 73 x Fk(4)p Fj(\036)1280 3748
y Fi(4)1336 3772 y Fh(\000)g Fj(\014)1470 3748 y Fi(2)1803
3772 y Fk(0)345 b Fh(\000)p Fk(16)17 b(+)h Fj(\014)326
b Fk(2)p Fj(\015)1286 3881 y Fk(0)263 b Fh(\000)1656
3808 y Ff(p)p 1738 3808 V 1738 3881 a Fk(4)p Fj(\036)1829
3857 y Fi(4)1885 3881 y Fh(\000)18 b Fj(\014)2019 3857
y Fi(2)2296 3881 y Fk(2)p Fj(\015)358 b Fk(16)17 b Fh(\000)i
Fj(\014)3090 3496 y Ff(1)3090 3642 y(C)3090 3692 y(C)3090
3745 y(A)731 4184 y Fj(B)27 b Fk(=)944 4128 y(1)p 919
4165 91 4 v 919 4241 a(8)p Fj(\036)1034 3967 y Ff(0)1034
4113 y(B)1034 4163 y(B)1034 4216 y(@)1221 4024 y Fk(16)18
b Fh(\000)g Fj(\014)331 b Fk(2)p Fj(\015)5 b(!)214 b
Fh(\000)2205 3951 y Ff(p)p 2287 3951 319 4 v 2287 4024
a Fk(4)p Fj(\036)2378 4000 y Fi(4)2434 4024 y Fh(\000)18
b Fj(\014)2568 4000 y Fi(2)2868 4024 y Fk(0)1267 4133
y(2)p Fj(\015)11 b Fk(\026)-48 b Fj(!)297 b Fh(\000)p
Fk(16)17 b(+)h Fj(\014)350 b Fk(0)2689 4060 y Ff(p)p
2772 4060 V 73 x Fk(4)p Fj(\036)2863 4109 y Fi(4)2918
4133 y Fh(\000)18 b Fj(\014)3052 4109 y Fi(2)1106 4243
y Fh(\000)1171 4170 y Ff(p)p 1254 4170 V 73 x Fk(4)p
Fj(\036)1345 4219 y Fi(4)1401 4243 y Fh(\000)g Fj(\014)1535
4219 y Fi(2)1835 4243 y Fk(0)378 b(16)17 b(+)h Fj(\014)331
b Fk(2)p Fj(\015)5 b(!)1319 4352 y Fk(0)1655 4279 y Ff(p)p
1738 4279 V 73 x Fk(4)p Fj(\036)1829 4328 y Fi(4)1885
4352 y Fh(\000)18 b Fj(\014)2019 4328 y Fi(2)2301 4352
y Fk(2)p Fj(\015)11 b Fk(\026)-48 b Fj(!)296 b Fh(\000)p
Fk(16)17 b Fh(\000)h Fj(\014)3090 3967 y Ff(1)3090 4113
y(C)3090 4163 y(C)3090 4216 y(A)515 4541 y Fb(wher)l(e)30
b Fj(\015)797 4511 y Fi(2)857 4541 y Fk(=)22 b Fh(\000)p
Fj(\036)1058 4511 y Fi(4)1113 4541 y Fk(+)17 b(20)p Fj(\036)1328
4511 y Fi(2)1382 4541 y Fh(\000)g Fk(64)p Fb(,)28 b Fj(\014)1652
4511 y Fi(2)1713 4541 y Fk(=)23 b(16)p Fj(\036)1934 4511
y Fi(2)1988 4541 y Fh(\000)16 b Fj(\015)2117 4511 y Fi(2)2154
4541 y Fk(\(1)h(+)g Fj(!)s Fk(\)\(1)g(+)24 b(\026)-49
b Fj(!)s Fk(\))p Fb(,)30 b Fh(j)p Fj(!)s Fh(j)23 b Fk(=)f(1)p
Fb(,)30 b Fj(\036)23 b Fh(2)g Fk([2)p Fj(;)14 b Fk(4])p
Fb(.)639 4640 y(F)-6 b(or)22 b Fj(\036)h Fk(=)g(2)e Fb(the)g(r)l(epr)l
(esentation)h(de)l(c)l(omp)l(oses)g(into)g(dir)l(e)l(ct)f(sum)g(of)h
(four)g(one-dimensional)515 4740 y(r)l(epr)l(esenations,)31
b Fj(A)23 b Fk(=)g Fh(\006)p Fk(1)p Fj(=)p Fk(2)p Fb(,)28
b Fj(B)f Fk(=)c Fh(\007)p Fk(3)p Fj(=)p Fk(2)k Fb(and)k
Fj(A)23 b Fk(=)g Fh(\006)p Fk(3)p Fj(=)p Fk(2)p Fb(,)28
b Fj(B)f Fk(=)c Fh(\007)p Fk(1)p Fj(=)p Fk(2)p Fb(.)639
4840 y(F)-6 b(or)42 b Fj(\036)i Fk(=)f(2)1049 4771 y
Fh(p)p 1117 4771 42 4 v 1117 4840 a Fk(2)p Fb(,)h Fj(!)j
Fk(=)c(1)d Fb(the)h(r)l(epr)l(esentations)h(de)l(c)l(omp)l(oses)g(into)
f(dir)l(e)l(ct)h(sum)e(of)515 4939 y(two)34 b(one-dimensional)j(r)l
(epr)l(esentations)e Fj(A)d Fk(=)f Fj(B)36 b Fk(=)c Fh(\006)p
Fk(1)p Fj(=)p Fk(2)g Fb(and)j(one)g(irr)l(e)l(ducible)h(two-)1926
5255 y Fk(1)p eop end
%%Page: 2 2
TeXDict begin 2 1 bop 515 523 a Fb(dimensional)31 b(r)l(epr)l
(esentaion)1199 756 y Fj(A)23 b Fk(=)1372 639 y Ff(\022)1433
706 y Fh(\000)1498 637 y(p)p 1566 637 42 4 v 1566 706
a Fk(2)83 b(1)p Fj(=)p Fk(2)1458 811 y(1)p Fj(=)p Fk(2)1698
742 y Fh(p)p 1767 742 V 69 x Fk(2)1816 639 y Ff(\023)1890
756 y Fj(;)99 b(B)27 b Fk(=)2190 639 y Ff(\022)2258 637
y Fh(p)p 2327 637 V 69 x Fk(2)115 b(1)p Fj(=)p Fk(2)2251
811 y(1)p Fj(=)p Fk(2)82 b Fh(\000)2524 742 y(p)p 2592
742 V 2592 811 a Fk(2)2634 639 y Ff(\023)515 995 y Fb(with)30
b(the)g(sp)l(e)l(ctrum)f(of)i Fj(A)f Fb(and)g Fj(B)k
Fb(e)l(qual)c(to)f Fh(f\000)p Fk(3)p Fj(=)p Fk(2)p Fj(;)14
b Fk(3)p Fj(=)p Fk(2)p Fh(g)639 1094 y Fb(F)-6 b(or)33
b Fj(\036)28 b Fk(=)f(4)32 b Fb(the)h(r)l(epr)l(esentation)f(de)l(c)l
(omp)l(oses)i(into)f(dir)l(e)l(ct)f(sum)g(of)h(two)g(irr)l(e)l(ducible)
515 1194 y(two-dimensional)e(r)l(epr)l(esentations,)1148
1427 y Fj(A)23 b Fk(=)1321 1310 y Ff(\022)1382 1377 y
Fk(1)p Fj(=)p Fk(2)155 b(0)1423 1476 y(0)125 b Fh(\000)p
Fk(3)p Fj(=)p Fk(2)1779 1310 y Ff(\023)1854 1427 y Fj(;)98
b(B)28 b Fk(=)2153 1310 y Ff(\022)2290 1377 y Fk(0)2491
1308 y Fh(p)p 2560 1308 V 69 x Fk(3)p Fj(=)p Fk(2)2214
1413 y Fh(p)p 2283 1413 V 69 x Fk(3)p Fj(=)p Fk(2)158
b(1)2685 1310 y Ff(\023)1162 1615 y Fj(\033)s Fk(\()p
Fj(A)p Fk(\))24 b(=)f Fh(f)p Fk(1)p Fj(=)p Fk(2)p Fj(;)14
b Fh(\000)p Fk(3)p Fj(=)p Fk(2)p Fh(g)p Fj(;)94 b(\033)s
Fk(\()p Fj(B)t Fk(\))25 b(=)d Fh(f\000)p Fk(1)p Fj(=)p
Fk(2)p Fj(;)14 b Fk(3)p Fj(=)p Fk(2)p Fh(g)515 1797 y
Fb(and)1083 2015 y Fj(A)24 b Fk(=)1256 1897 y Ff(\022)1317
1964 y Fh(\000)p Fk(1)p Fj(=)p Fk(2)123 b(0)1391 2064
y(0)157 b(3)p Fj(=)p Fk(2)1714 1897 y Ff(\023)1789 2015
y Fj(;)99 b(B)27 b Fk(=)2089 1897 y Ff(\022)2258 1964
y Fk(0)191 b Fh(\000)2556 1895 y(p)p 2625 1895 V 69 x
Fk(3)o Fj(=)p Fk(2)2150 2069 y Fh(\000)2215 2000 y(p)p
2283 2000 V 2283 2069 a Fk(3)p Fj(=)p Fk(2)158 b Fh(\000)p
Fk(1)2749 1897 y Ff(\023)1162 2202 y Fj(\033)s Fk(\()p
Fj(A)p Fk(\))24 b(=)f Fh(f\000)p Fk(1)p Fj(=)p Fk(2)p
Fj(;)14 b Fk(3)p Fj(=)p Fk(2)p Fh(g)p Fj(;)94 b(\033)s
Fk(\()p Fj(B)t Fk(\))25 b(=)d Fh(f)p Fk(1)p Fj(=)p Fk(2)p
Fj(;)14 b Fh(\000)p Fk(3)p Fj(=)p Fk(2)p Fh(g)639 2385
y Fb(F)-6 b(or)27 b(al)t(l)h(other)f(p)l(airs)h Fk(\()p
Fj(\036;)14 b(!)s Fk(\))p Fb(,)28 b Fj(\036)c Fh(2)f
Fk(\(2)p Fj(;)14 b Fk(4\))p Fb(,)27 b Fh(j)p Fj(!)s Fh(j)c
Fk(=)g(1)j Fb(the)h(r)l(epr)l(esentation)g(is)g(irr)l(e)l(ducible)515
2484 y(with)j Fj(\033)s Fk(\()p Fj(A)p Fk(\))24 b(=)f
Fj(\033)s Fk(\()p Fj(B)t Fk(\))h(=)f Fh(f\006)p Fk(1)p
Fj(=)p Fk(2)p Fj(;)14 b Fh(\006)p Fk(3)p Fj(=)p Fk(2)p
Fh(g)p Fb(.)639 2584 y(Liste)l(d)30 b(ab)l(ove)h(ar)l(e)f(al)t(l)h(irr)
l(e)l(ducible)g(r)l(epr)l(esentations)f(up)g(to)g(a)g(unitary)g(e)l
(quivalenc)l(e.)515 2858 y Fa(References)515 3040 y Fk([1])41
b(M.A.Vlasenk)n(o,)23 b(A.S.Mellit,)i(Y)-7 b(u.Samoilenk)n(o.)22
b Fb(On)j(algebr)l(as)i(gener)l(ate)l(d)f(by)g(line)l(arly)644
3140 y(c)l(onne)l(cte)l(d)32 b(gener)l(ators)h(with)g(a)g(given)g(sp)l
(e)l(ctrum)p Fk(,)e(F)-7 b(unct.)31 b(Anal.)g(Appl.)g
Fc(38)f Fk(\(2004\),)644 3239 y(no.)d(2.)515 3406 y([2])41
b(V.Ostroskyi,)c(Y)-7 b(u.Samoilenk)n(o.)36 b Fb(Intr)l(o)l(duction)i
(to)g(the)g(the)l(ory)h(of)g(r)l(epr)l(esentations)644
3505 y(of)32 b(\014nitely)f(pr)l(esente)l(d)g(*-algebr)l(as.)h(R)l(epr)
l(esentations)f(by)g(buonde)l(d)h(op)l(er)l(ators)p Fk(,)e(Rev.)644
3605 y(Math.&)h(Math.)h(Ph)n(ys.,)g(1999,)f(v)n(ol.)g(11,)h(pp.)g
(1{261,)e(Gordon)h(&)g(Breac)n(h,)h(London)644 3704 y(1999.)515
3870 y([3])41 b(A.S.Mellit.)31 b Fb(On)g(the)h(c)l(ase)h(wher)l(e)f(a)h
(sum)e(of)i(thr)l(e)l(e)e(p)l(artial)j(maps)e(is)g(e)l(qual)h(to)f(zer)
l(o)p Fk(,)644 3970 y(Ukr.)27 b(Math.)h(J.,)f Fc(55)h
Fk(\(2003\),)e(no.)h(9,)h(pp.)g(1277{1283.)1926 5255
y(2)p eop end
%%Trailer

userdict /end-hook known{end-hook}if
%%EOF