% $Date: 2003/10/28 21:59:21 $ $Author: nthiery $ $Revision: 1.1.1.2 $

\begin{Mhelppage}{SgDimRep}
  {V. Prosper}%
  \begin{MInfo}
    \eng{computes the dimension of a representation}
  \end{MInfo}
  

\begin{MCalls}
  \Mcall{part}
\end{MCalls}

\begin{MParameters}
  \param{part}
  \eng{any list denoting a (skew) partition} 
\end{MParameters}

\begin{MIntro}
  \eng{
The {\Mthis}   function   computes  the  dimension  of  the  irreducible
representation of  index  \Mex{part}, for  the  symmetric  group  of order the
weight of \Mex{part}.

When part  is  a  skew  partition, it  computes  the  dimension  of  the
representation indexed by the skew partition
\Mmath{\Mex{part[1]/part[2]}}{\mathtt{part}_1/\mathtt{part}_2}.

Adding the parameter \Mex{q}, it computes the specialization of
\Mmath{\Mex{s[part]}}{\mathtt{s[part]}}  or
\Mmath{\Mex{s[part[1]/part[2]]}}{\mathtt{s[part_1/part_2]}} in
\Mmath{x1=1, x2=\Mex{q}, ...}{x_1=1, x_2=\mathtt{q}, \ldots}.
}
\end{MIntro}

\begin{MExample}{ex1}
\begin{Mexin}
muEC::SG::SgDimRep( [4,4,3,2,1,1,1] );
\end{Mexin}
\begin{Mexout}
                            512512
\end{Mexout}
\begin{Mexin}
muEC::SG::SgDimRep( [[4,2,1,1], [2,1]] );
\end{Mexin}
\begin{Mexout}
                              30
\end{Mexout}
%
\begin{Mexin}
muEC::SG::SgDimRep([[4,2,1,1], [2,1]], q);
\end{Mexin}
\begin{Mexout}
                2        2            2    3    4
        q (q + q  + 1) (q  + 1) (q + q  + q  + q  + 1)
\end{Mexout}
% \begin{Mexout}[hide]
     % q*(q^2 + 1)*(q + q^2 + 1)*(q + q^2 + q^3 + q^4 + 1)
% \end{Mexout}
\end{MExample}

\MRelatedFunctions{SgCharTable}
\end{Mhelppage}
