% $Date: 2003/10/28 21:59:22 $ $Author: nthiery $ $Revision: 1.1.1.2 $

\begin{Mhelppage}{Char2Sf}{V. Prosper}

  \begin{MInfo}
    \eng{converts a virtual character into a symmetric function}
  \end{MInfo}

  \begin{MCalls}
    \Mcall{expr}
  \end{MCalls}

  \begin{MParameters}
    \param{expr}
    \eng{any linear combination of \Mex{cl[part]} for any partition part} 
  \end{MParameters}

  \begin{MIntro}
    \eng{The {\Mthis} function converts a virtual character into a
      symmetric function expressed on \Mex{p}-basis.
      
      We denote by \Mex{cl[part]}, where \Mex{part} is a partition,
      the class function on the symmetric group that is evaluated to 1
      for permutations with cycletype \Mex{part}, and 0 otherwise.
      
      The {\Mthis} function realizes the isomorphism between class
      functions on the symmetric group of degree \Mex{n} and
      homogeneous symmetric functions of degree \Mex{n}.  }
  \end{MIntro}

\begin{MExample}{ex1}
\begin{Mexin}
muEC::SYMF::Char2Sf( cl[5,3,1,1] )
\end{Mexin}
\begin{Mexout}
                         p[5, 3, 1, 1]
                         -------------
                               30
\end{Mexout}
% \begin{Mexout}[hide]
                     % p[5, 3, 1, 1]*1/30
% \end{Mexout}
\end{MExample}

\MRelatedFunctions{SfInternal,SfPlethysm,Sf2Char,SfZee}
\end{Mhelppage}
