% $Date: 2003/09/15 16:37:45 $ $Author: nthiery $ $Revision: 1.1.1.1 $

\begin{Mhelppage}{SgCharTable}{V. Prosper}

  \begin{MInfo}
    \eng{computes the table of characters}
  \end{MInfo}
  
  \begin{MCalls}
    \Mcall{n\Mopt{,part1}\Mopt{,part2}}
    \Mcall{n\Mopt{,index}}
  \end{MCalls}

  \begin{MParameters}
    \param{n}
    \eng{any positive integer denoting the degree of a symmetric group}
    \param{part1, part2}
    \eng{any lists denoting partitions}
  \end{MParameters}

  \begin{MIntro}
    \eng{The {\Mthis} gives the table of characters for the symmetric
      group of order \Mex{n}.  Let \Mex{t} be this matrix,
      \Mex{part1}, \Mex{part2} be two partitions of \Mex{n}, of index
      \Mmath{i}{i}, \Mmath{j}{j} in the list of partitions
      \Mex{{\Mthis}(n, index)}, then
      \Mmath{\Mex{t}[i,j]}{\mathtt{t}[i,j]} is equal to the value of
      the irreducible character of index \Mex{part1} on the conjugacy
      class indexed by \Mex{part2}.  }
  \end{MIntro}

\begin{MExample}{ex1}
\begin{Mexin}
muEC::SG::SgCharTable( 3 );
\end{Mexin}
\begin{Mexout}
                        +-           -+
                        |   1,  1, 1  |
                        |             |
                        |  -1,  0, 2  |
                        |             |
                        |   1, -1, 1  |
                        +-           -+
\end{Mexout}
% \begin{Mexout}[hide]
    % array(1..3, 1..3, (1,1) = 1,  (1,2) = 1,  (1,3) = 1,
    %                   (2,1) = -1, (2,2) = 0,  (2,3) = 2,
    %                   (3,1) = 1,  (3,2) = -1, (3,3) = 1 )
% \end{Mexout}
\begin{Mexin}
muEC::SG::SgCharTable( 3, index );
\end{Mexin}
\begin{Mexout}
                   [[3], [2, 1], [1, 1, 1]]
\end{Mexout}
\begin{Mexin}
muEC::SG::SgCharTable(3, [2,1], [1,1,1]);
\end{Mexin}
\begin{Mexout}
                               2
\end{Mexout}
\end{MExample}

\MRelatedFunctions{TYP::IsPart}
\end{Mhelppage}
