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defs.tex
\makeatletter \def\thmhead@my#1#2#3{% \thmname{#1}\thmnumber{\@ifnotempty{#1}{ }\@upn{#2}}% \thmnote{ {\the\thm@notefont#3}}% } \let\thmhead\thmhead@my \def\@makechapterhead#1{% \vspace*{0\p@}% {\parindent \z@ \raggedright \normalfont \ifnum \c@secnumdepth >\m@ne \huge\bfseries \@chapapp\space \thechapter \par\nobreak \vskip 20\p@ \fi \interlinepenalty\@M \Huge \bfseries #1\par\nobreak \vskip 60\p@ }} \def\@makeschapterhead#1{% \vspace*{0\p@}% {\parindent \z@ \raggedright \normalfont \interlinepenalty\@M \Huge \bfseries #1\par\nobreak \vskip 40\p@ }} \renewcommand\section{\clearpage\@startsection {section}{1}{\z@}% {-3.5ex \@plus -1ex \@minus -.2ex}% {2.3ex \@plus.2ex}% {\normalfont\Large\bfseries}} \makeatother \newcommand{\tstr}{\vrule width0pt height10pt depth 5pt} \newcommand{\bbone}{\mathbf{1}} \newcommand{\pro}{\mathord{\text{\textup{pro-}}}} \newcommand{\id}{\mathord{\text{\textup{id}}}} \DeclareMathOperator{\rep}{Rep} \DeclareMathOperator{\srep}{\ast-Rep} \DeclareMathOperator{\irrep}{Irrep} \DeclareMathOperator{\sirrep}{\ast-Irrep} \DeclareMathOperator{\sfdrep}{\ast-f.d.Rep} \DeclareMathOperator{\ad}{ad} \DeclareMathOperator{\tr}{Tr} \DeclareMathOperator{\im}{Im} \DeclareMathOperator{\diag}{diag} \DeclareMathOperator{\const}{const} \DeclareMathOperator{\wlim}{w-lim} %\DeclareMathOperator{\id}{id} \DeclareMathOperator{\supp}{supp} \DeclareMathOperator{\ls}{span} \DeclareMathOperator{\Lip}{Lip} \DeclareMathOperator{\diam}{diam} \DeclareMathOperator{\pr}{pr} \let\emptyset\varnothing \newcommand{\tenz}{T_{ij}^{kl}} \newcommand{\otenz}{T_{ik}^{lj}} \newcommand{\lm}{\lambda_{ij}} \newcommand{\lf}{\alpha_{ij}} \newcommand{\qu}{q_{ij}} \newcommand{\hb}{\mathcal{H}} \newcommand{\ub}{\mathcal{U}} \newcommand{\tpr}{e_{i}\otimes e_{j}} \newcommand{\otpr}{e_{j}\otimes e_{i}} \newcommand{\alp}{\alpha^{\pi}(i,j)} \newcommand{\alg}{\mathcal{U}(A,\Lambda)} \newcommand{\tbig}{T_{1}T_{2}\ , \cdots\ ,\ T_{n}} \newcommand{\llll}{\lambda} \newcommand{\h}{\ensuremath{\mathcal{H}}} \newcommand{\ca}{\ensuremath{C^*}} \newcommand {\base }{e_{(\lambda_{k},\mu_{k})}} \newcommand {\basep}{e_{(\lambda_{k+1},\mu_{k+1})}} \newcommand {\basem}{e_{(\lambda_{k-1},\mu_{k-1})}} \newcommand {\baseJ}{e_{(\lambda_{J-1},\mu_{J-1})}} \newcommand {\basej}{e_{(\lambda_{j+1},\mu_{j+1})}} \newcommand{\p}{p^{3}(1-p^{2})^{-1}} \newcommand{\ddd}{\Delta_{\nu} = } \newcommand{\setunit}{\setlength{\unitlength}{1pt}} \def\coxninf{% \raise.5ex\hbox{\lower7pt\hbox{% \setunit \begin{picture}(60.00,10.00)(-5,-7) \put(00.00,00.00){\circle*{3.00}} \put(0.00,00.00){\line(1,0){15}} \put(15.00,00.00){\circle*{3.00}} \put(30.00,00.00){\circle*{3.00}} \put(50.00,00.00){\circle*{3.00}} \put(7.5,2.0){\makebox(0,0)[b]{$\scriptstyle \infty$}} \put(0,-3){\makebox(0,0)[t]{$\scriptstyle u$}} \put(15,-3){\makebox(0,0)[t]{$\scriptstyle v$}} \put(32,-3){\makebox(0,0)[t]{$\scriptstyle u_1$}} \put(52,-3){\makebox(0,0)[t]{$\scriptstyle u_n$}} \put(40,0){\makebox(0,0)[cc]{$\ldots$}} \end{picture}}}% } \def\twopointinf{ \raise.5ex\hbox{\hbox{% \setunit \begin{picture}(27.00,5.00)(-5,00) \put(00.00,00.00){\circle*{3.00}} \put(0.00,00.00){\line(1,0){15}} \put(15.00,00.00){\circle*{3.00}} \put(7.5,2.0){\makebox(0,0)[b]{$\scriptstyle \infty$}} \end{picture}}}% } \def\edgeright#1#2{% \raise.5ex\hbox{\lower7pt\hbox{% \setunit \begin{picture}(25.00,5.00)(-5,-7) \put(00.00,00.00){\circle*{3.00}} \put(0.00,00.00){\vector(1,0){14}} \put(15.00,00.00){\circle*{3.00}} \put(0,-10){\makebox(0,0)[b]{$\scriptstyle #1$}} \put(15,-10){\makebox(0,0)[b]{$\scriptstyle #2$}} \end{picture}}}% } \def\edgeleft#1#2{% \raise.5ex\hbox{\lower7pt\hbox{% \setunit \begin{picture}(30.00,5.00)(-5,-7) \put(00.00,00.00){\circle*{3.00}} \put(15.00,00.00){\vector(-1,0){14}} \put(15.00,00.00){\circle*{3.00}} \put(0,-10){\makebox(0,0)[b]{$\scriptstyle #1$}} \put(15,-10){\makebox(0,0)[b]{$\scriptstyle #2$}} \end{picture}}}% } \def\onepoint#1{% \raise.5ex\hbox{\lower7pt\hbox{% \setunit \begin{picture}(10.00,5.00)(-5,-7) \put(00.00,00.00){\circle*{3.00}} \put(0,-10){\makebox(0,0)[b]{$\scriptstyle #1$}} \end{picture}}}% } \def\ear#1{% \raise.5ex\hbox{\lower7pt\hbox{% \setunit \begin{picture}(10.00,18.00)(-5,-7) \put(00.00,00.00){\circle*{3.00}} \put(0.00,00.00){\bezier{20}(0,0)(-6,6)(-3,9)} \put(0.00,00.00){\bezier{20}(-3,9)(00,12)(3,9)} \put(0.00,00.00){\bezier{20}(0,0)(6,6)(3,9)} \put(0,-10){\makebox(0,0)[b]{$\scriptstyle #1$}} \end{picture}}}% } \def\edge#1#2{% \raise.5ex\hbox{\lower7pt\hbox{% \setunit \begin{picture}(25.00,5.00)(-5,-7) \put(00.00,00.00){\circle*{3.00}} \put(0.00,00.00){\line(1,0){15}} \put(15.00,00.00){\circle*{3.00}} \put(0,-10){\makebox(0,0)[b]{$\scriptstyle #1$}} \put(15,-10){\makebox(0,0)[b]{$\scriptstyle #2$}} \end{picture}}}% } \def\onepointx{% \raise.5ex\hbox{\hbox{% \setunit \begin{picture}(12.00,5.00)(-5,00) \put(00.00,00.00){\circle*{3.00}} \end{picture}}}% } \def\earx{% \raise.5ex\hbox{\hbox{% \setunit \begin{picture}(12.00,11.00)(-5,00) \put(00.00,00.00){\circle*{3.00}} \put(0.00,00.00){\bezier{20}(0,0)(-6,6)(-3,9)} \put(0.00,00.00){\bezier{20}(-3,9)(00,12)(3,9)} \put(0.00,00.00){\bezier{20}(0,0)(6,6)(3,9)} \end{picture}}}% } \def\edgex{% \raise.5ex\hbox{\hbox{% \setunit \begin{picture}(27.00,5.00)(-5,00) \put(00.00,00.00){\circle*{3.00}} \put(0.00,00.00){\line(1,0){15}} \put(15.00,00.00){\circle*{3.00}} \end{picture}}}% } \def\twoedge#1#2#3{% \raise.5ex\hbox{\lower7pt\hbox{% \setunit \begin{picture}(40.00,00.00)(-5,-7) \put(00.00,00.00){\circle*{3.00}} \put(0.00,00.00){\line(1,0){15}} \put(15.00,00.00){\circle*{3.00}} \put(15.00,00.00){\line(1,0){15}} \put(30.00,00.00){\circle*{3.00}} \put(0,-10){\makebox(0,0)[b]{$\scriptstyle #1$}} \put(15,-10){\makebox(0,0)[b]{$\scriptstyle #2$}} \put(30,-10){\makebox(0,0)[b]{$\scriptstyle #3$}} \end{picture}}}% } \def\earedge{% \raise.5ex\hbox{\hbox{% \setunit \begin{picture}(27.00,11.00)(-5,0) \put(00.00,00.00){\circle*{3.00}} \put(0.00,00.00){\bezier{20}(0,0)(-6,6)(-3,9)} \put(0.00,00.00){\bezier{20}(-3,9)(00,12)(3,9)} \put(0.00,00.00){\bezier{20}(0,0)(6,6)(3,9)} \put(0.00,00.00){\line(1,0){15}} \put(15.00,00.00){\circle*{3.00}} \end{picture}}}% } \def\twovec{% \raise.5ex\hbox{\hbox{% \setunit \begin{picture}(42.00,00.00)(-5,0) \put(00.00,00.00){\circle*{3.00}} \put(0.00,00.00){\vector(1,0){14}} \put(15.00,00.00){\circle*{3.00}} \put(15.00,00.00){\vector(1,0){14}} \put(30.00,00.00){\circle*{3.00}} \end{picture}}}% } \def\chainl#1#2#3{% \raise.5ex\hbox{\lower7pt\hbox{% \setunit \begin{picture}(70.00,10.00)(-20,-7) \put(00.00,00.00){\circle*{3.00}} \put(00.00,00.00){\line(1,0){15}} \put(15.00,00.00){\circle*{3.00}} \put(15.00,00.00){\line(1,0){15}} \put(30.00,00.00){\circle*{3.00}} \put(00,-10){\makebox(0,0)[b]{$\scriptstyle #1$}} \put(15,-10){\makebox(0,0)[b]{$\scriptstyle #2$}} \put(30,-10){\makebox(0,0)[b]{$\scriptstyle #3$}} \put(-10,-0.5){\makebox(0,0)[b]{$\ldots$}} \put(41,-0.5){\makebox(0,0)[b]{$\ldots$}} \end{picture}}}% } \def\cycle#1#2#3{% \raise.5ex\hbox{\lower7pt\hbox{% \setunit \begin{picture}(60.00,12.00)(-5,-7) \put(00.00,00.00){\circle*{3.00}} \put(00.00,00.00){\line(1,0){15}} \put(15.00,00.00){\circle*{3.00}} \put(50.00,00.00){\circle*{3.00}} \put(35.00,00.00){\line(1,0){15}} \put(35.00,00.00){\circle*{3.00}} \put(0.00,00.00){\bezier{100}(0,0)(25,10)(50,00)} \put(00,-10){\makebox(0,0)[b]{$\scriptstyle #1$}} \put(15,-10){\makebox(0,0)[b]{$\scriptstyle #2$}} \put(50,-10){\makebox(0,0)[b]{$\scriptstyle #3$}} \put(25,-0.5){\makebox(0,0)[b]{$\ldots$}} \end{picture}}}% } \def\earchear#1#2{% \raise.5ex\hbox{\lower12pt\hbox{% \setunit \begin{picture}(60.00,18.00)(-5,-12) \put(00.00,00.00){\circle*{3.00}} \put(0.00,00.00){\bezier{20}(0,0)(-6,6)(-3,9)} \put(0.00,00.00){\bezier{20}(-3,9)(00,12)(3,9)} \put(0.00,00.00){\bezier{20}(0,0)(6,6)(3,9)} \put(0.00,00.00){\line(1,0){15}} \put(15.00,00.00){\circle*{3.00}} \put(35.00,00.00){\circle*{3.00}} \put(35.00,00.00){\line(1,0){15}} \put(50.00,00.00){\circle*{3.00}} \put(50.00,00.00){\bezier{20}(0,0)(-6,6)(-3,9)} \put(50.00,00.00){\bezier{20}(-3,9)(00,12)(3,9)} \put(50.00,00.00){\bezier{20}(0,0)(6,6)(3,9)} \put(0,-17){\makebox(0,0)[b]{$\textstyle #1$}} \put(50,-17){\makebox(0,0)[b]{$\textstyle #2$}} \put(25,-0.5){\makebox(0,0)[b]{$\ldots$}} \end{picture}}}% } \def\earch#1#2{% \raise.5ex\hbox{\lower12pt\hbox{% \setunit \begin{picture}(60.00,18.00)(-5,-12) \put(00.00,00.00){\circle*{3.00}} \put(0.00,00.00){\bezier{20}(0,0)(-6,6)(-3,9)} \put(0.00,00.00){\bezier{20}(-3,9)(00,12)(3,9)} \put(0.00,00.00){\bezier{20}(0,0)(6,6)(3,9)} \put(0.00,00.00){\line(1,0){15}} \put(15.00,00.00){\circle*{3.00}} \put(35.00,00.00){\circle*{3.00}} \put(35.00,00.00){\line(1,0){15}} \put(50.00,00.00){\circle*{3.00}} \put(0,-17){\makebox(0,0)[b]{$\textstyle #1$}} \put(50,-17){\makebox(0,0)[b]{$\textstyle #2$}} \put(25,-0.5){\makebox(0,0)[b]{$\ldots$}} \end{picture}}}% } \def\ch#1#2{% \raise.5ex\hbox{\lower12pt\hbox{% \setunit \begin{picture}(60.00,10.00)(-5,-12) \put(00.00,00.00){\circle*{3.00}} \put(0.00,00.00){\line(1,0){15}} \put(15.00,00.00){\circle*{3.00}} \put(35.00,00.00){\circle*{3.00}} \put(35.00,00.00){\line(1,0){15}} \put(50.00,00.00){\circle*{3.00}} \put(0,-17){\makebox(0,0)[b]{$\textstyle #1$}} \put(50,-17){\makebox(0,0)[b]{$\textstyle #2$}} \put(25,-0.5){\makebox(0,0)[b]{$\ldots$}} \end{picture}}}% } \def\coxetertwoedge#1#2{% \raise.5ex\hbox{\hbox{% \setunit \begin{picture}(40.00,06)(-5.0,0.0) \put(00.00,00.00){\circle*{3.00}} \put(0.00,00.00){\line(1,0){15}} \put(15.00,00.00){\circle*{3.00}} \put(30.00,00.00){\circle*{3.00}} \put(15.00,00.00){\line(1,0){15}} \put(07.5,02){\makebox(0,0)[b]{$\scriptstyle #1$}} \put(22.5,02){\makebox(0,0)[b]{$\scriptstyle #2$}} \end{picture}}}% } \def\coxetertriangle#1#2#3{% \raise.5ex\hbox{\lower6pt\hbox{% \setunit \begin{picture}(30.00,18.00)(-5,-6) \put(00.00,00.00){\circle*{3.00}} \put(0.00,00.00){\line(1,0){20}} \put(20.00,00.00){\circle*{3.00}} \put(10.00,10.00){\circle*{3.00}} \put(00.00,00.00){\line(1,1){10}} \put(10.00,10.00){\line(1,-1){10}} \put(10,-5){\makebox(0,0)[b]{$\scriptstyle #1$}} \put(00,05){\makebox(0,0)[b]{$\scriptstyle #2$}} \put(20,05){\makebox(0,0)[b]{$\scriptstyle #3$}} \end{picture}}}% } %%% Local Variables: %%% mode: latex %%% TeX-master: "thesis" %%% End: