FUNCTION: Char2Sf - convert a virtual character into a symmetric function

CALLING SEQUENCE:

Char2Sf(expr)

SYMF[Char2Sf](expr)

PARAMETERS:

expr = any linear combination of cl[part] for any partition part

SYNOPSIS:

• The Char2Sf function converts a virtual character into a symmetric function expressed on p-basis.

• We denote by cl[part], where part is a partition, the class function on the symmetric group that is evaluated to 1 for permutations with cycle- type part, and 0 otherwise.

• The Char2Sf function realizes the isomorphism between class functions on the symmetric group of degree n and homogeneous symmetric functions of degree n.

• Whenever there is a conflict between the function name Char2Sf and another name used in the same session, use the long form SYMF['Char2Sf'].

EXAMPLES:

> with(SYMF):
> Char2Sf(cl[5,3,1,1]);
 
                                              2
                                 1/30 p5 p3 p1