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DEFS.TEX
\theoremstyle{plain} \newtheorem{theorem}{Theorem} \newtheorem{proposition}{Proposition} \newtheorem{lemma}{Lemma} \newtheorem{corollary}{Corollary} \newtheorem{definition}{Definition} \theoremstyle{remark} \newtheorem{example}{Example} \newtheorem{remark}{Remark} \newcommand{\bbone}{\mathbf{1}} \DeclareMathOperator{\rep}{Rep} \DeclareMathOperator{\irrep}{Irrep} \DeclareMathOperator{\range}{R} \DeclareMathOperator{\orb}{Orb} \DeclareMathOperator{\ad}{ad} \DeclareMathOperator{\tr}{Tr} \DeclareMathOperator{\im}{Im} \DeclareMathOperator{\diag}{diag} \DeclareMathOperator{\sign}{sign} \DeclareMathOperator{\const}{const} \DeclareMathOperator{\wlim}{w-lim} \DeclareMathOperator{\id}{id} \newcommand{\coxninf}{\mathop{\bullet}\limits_u \stackrel{\infty}{-} \mathop{\bullet}\limits_v\quad \mathop{\bullet}\limits_{u_1}\ \cdots \ \mathop{\bullet}\limits_{u_n}} \newcommand{\twopointinf}{\mathop{\bullet}\stackrel{\infty}{-} \mathop{\bullet}} \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\edgeright#1#2{% \raise.5ex\hbox{\lower12pt\hbox{% \setunit \begin{picture}(30.00,15.00)(-5,-12) \put(00.00,00.00){\circle*{3.00}} \put(0.00,00.00){\vector(1,0){20}} \put(20.00,00.00){\circle*{3.00}} \put(0,-10){\makebox(0,0)[b]{$\scriptstyle #1$}} \put(20,-10){\makebox(0,0)[b]{$\scriptstyle #2$}} \end{picture}}}% } \def\edgeleft#1#2{% \raise.5ex\hbox{\lower12pt\hbox{% \setunit \begin{picture}(30.00,15.00)(-5,-12) \put(00.00,00.00){\circle*{3.00}} \put(20.00,00.00){\vector(-1,0){20}} \put(20.00,00.00){\circle*{3.00}} \put(0,-10){\makebox(0,0)[b]{$\scriptstyle #1$}} \put(20,-10){\makebox(0,0)[b]{$\scriptstyle #2$}} \end{picture}}}% } \def\onepoint#1{% \raise.5ex\hbox{\lower12pt\hbox{% \setunit \begin{picture}(10.00,15.00)(-5,-12) \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{\lower12pt\hbox{% \setunit \begin{picture}(10.00,25.00)(-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,-10){\makebox(0,0)[b]{$\scriptstyle #1$}} \end{picture}}}% } \def\edge#1#2{% \raise.5ex\hbox{\lower12pt\hbox{% \setunit \begin{picture}(30.00,15.00)(-5,-12) \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(0,-10){\makebox(0,0)[b]{$\scriptstyle #1$}} \put(20,-10){\makebox(0,0)[b]{$\scriptstyle #2$}} \end{picture}}}% } \def\onepointx{% \raise.5ex\hbox{\hbox{% \setunit \begin{picture}(10.00,5.00)(-5,00) \put(00.00,00.00){\circle*{3.00}} \end{picture}}}% } \def\earx{% \raise.5ex\hbox{\hbox{% \setunit \begin{picture}(10.00,12.00)(-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}(30.00,5.00)(-5,00) \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}} \end{picture}}}% } \def\twoedge#1#2#3{% \raise.5ex\hbox{\hbox{% \setunit \begin{picture}(50.00,00.00)(-5,0) \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(20.00,00.00){\line(1,0){20}} \put(40.00,00.00){\circle*{3.00}} \put(0,-10){\makebox(0,0)[b]{$\scriptstyle #1$}} \put(20,-10){\makebox(0,0)[b]{$\scriptstyle #2$}} \put(40,-10){\makebox(0,0)[b]{$\scriptstyle #3$}} \end{picture}}}% } \def\earedge{% \raise.5ex\hbox{\hbox{% \setunit \begin{picture}(30.00,12.00)(-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){20}} \put(20.00,00.00){\circle*{3.00}} \end{picture}}}% } \def\twovec{% \raise.5ex\hbox{\hbox{% \setunit \begin{picture}(50.00,00.00)(-5,0) \put(00.00,00.00){\circle*{3.00}} \put(0.00,00.00){\vector(1,0){20}} \put(20.00,00.00){\circle*{3.00}} \put(20.00,00.00){\vector(1,0){20}} \put(40.00,00.00){\circle*{3.00}} \end{picture}}}% } \def\chainl#1#2#3{% \raise.5ex\hbox{\lower12pt\hbox{% \setunit \begin{picture}(70.00,15.00)(-5,-12) \put(00.00,00.00){\circle*{3.00}} \put(00.00,00.00){\line(1,0){20}} \put(20.00,00.00){\circle*{3.00}} \put(20.00,00.00){\line(1,0){20}} \put(40.00,00.00){\circle*{3.00}} \put(00,-10){\makebox(0,0)[b]{$\scriptstyle #1$}} \put(20,-10){\makebox(0,0)[b]{$\scriptstyle #2$}} \put(40,-10){\makebox(0,0)[b]{$\scriptstyle #3$}} \put(-10,00){\makebox(0,0)[b]{$\scriptstyle \ldots$}} \put(50,00){\makebox(0,0)[b]{$\scriptstyle \ldots$}} \end{picture}}}% } \def\cycle#1#2#3{% \raise.5ex\hbox{\lower12pt\hbox{% \setunit \begin{picture}(70.00,15.00)(-5,-12) \put(00.00,00.00){\circle*{3.00}} \put(00.00,00.00){\line(1,0){20}} \put(20.00,00.00){\circle*{3.00}} \put(60.00,00.00){\circle*{3.00}} \put(40.00,00.00){\line(1,0){20}} \put(40.00,00.00){\circle*{3.00}} \put(0.00,00.00){\bezier{100}(0,0)(30,10)(60,00)} \put(00,-10){\makebox(0,0)[b]{$\scriptstyle #1$}} \put(20,-10){\makebox(0,0)[b]{$\scriptstyle #2$}} \put(60,-10){\makebox(0,0)[b]{$\scriptstyle #3$}} \put(30,00){\makebox(0,0)[b]{$\scriptstyle \ldots$}} \end{picture}}}% } \def\earchear#1#2{% \raise.5ex\hbox{\lower12pt\hbox{% \setunit \begin{picture}(30.00,25.00)(-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){20}} \put(20.00,00.00){\circle*{3.00}} \put(40.00,00.00){\circle*{3.00}} \put(40.00,00.00){\line(1,0){20}} \put(60.00,00.00){\circle*{3.00}} \put(60.00,00.00){\bezier{20}(0,0)(-6,6)(-3,9)} \put(60.00,00.00){\bezier{20}(-3,9)(00,12)(3,9)} \put(60.00,00.00){\bezier{20}(0,0)(6,6)(3,9)} \put(0,-15){\makebox(0,0)[b]{$\scriptstyle #1$}} \put(60,-15){\makebox(0,0)[b]{$\scriptstyle #2$}} \put(30,00){\makebox(0,0)[b]{$\scriptstyle 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\put(60,-15){\makebox(0,0)[b]{$\scriptstyle #2$}} \put(30,00){\makebox(0,0)[b]{$\scriptstyle \ldots$}} \end{picture}}}% }