% $Date: 2003/09/15 16:37:46 $ $Author: nthiery $ $Revision: 1.1.1.1 $

\begin{Mhelppage}{Sf2Char}%
  {V. Prosper}%
  \begin{MInfo}
    \eng{converts a symmetric function into a virtual character}
  \end{MInfo}
  

\begin{MCalls}
  \Mcall{sf}
\end{MCalls}

\begin{MParameters}
  \param{sf}
  \eng{any symmetric function} 
\end{MParameters}

\begin{MIntro}
  \eng{
The {\Mthis} function  converts  a  symmetric  function  into  a  virtual
character. This function is the inverse of \Mex{Char2Sf}.

The  {\Mthis}  function  realizes   the  isomorphism  between the  linear
space of homogeneous symmetric functions of degree \Mex{n} and class functions
on   the   symmetric   group   of   degree   \Mex{n}  (Frobenius  isomorphism).

The result is a linear combination of \Mex{cl[part]} where \Mex{part} is a
partition.
}
\end{MIntro}

\begin{MExample}{ex1}
\begin{Mexin}
muEC::SYMF::Sf2Char( s[3,1,1] );
\end{Mexin}
\begin{Mexout}
          cl[5] - 2 cl[2, 2, 1] + 6 cl[1, 1, 1, 1, 1]
\end{Mexout}
\begin{Mexin}
muEC::SYMF::Sf2Char( p[3]*s[3] - e[4] );
\end{Mexin}
\begin{Mexout}
cl[4] - cl[2, 2] - cl[3, 1] + 6 cl[3, 3] + cl[2, 1, 1] +

   3 cl[3, 2, 1] - cl[1, 1, 1, 1] + 3 cl[3, 1, 1, 1]
\end{Mexout}
\end{MExample}

\MRelatedFunctions{Char2Sf,SfInternal,SfPlethysm,SfZee}
\end{Mhelppage}
