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SYMF::Sf2Char -- converts a symmetric function into a virtual character

Call(s)


SYMF::Sf2Char(sf)

Parameters

sf- any symmetric function

Introduction

The SYMF::Sf2Char function converts a symmetric function into a virtual character. This function is the inverse of Char2Sf.

The SYMF::Sf2Char function realizes the isomorphism between the linear space of homogeneous symmetric functions of degree n and class functions on the symmetric group of degree n (Frobenius isomorphism).

The result is a linear combination of cl[part] where part is a partition.

Example 1

>> muEC::SYMF::Sf2Char( s[3,1,1] );
                cl[5] - 2 cl[2, 2, 1] + 6 cl[1, 1, 1, 1, 1]
>> muEC::SYMF::Sf2Char( p[3]*s[3] - e[4] );
      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]

Related Functions

Char2Sf, SfInternal, SfPlethysm, SfZee

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MuPAD Combinat, an open source algebraic combinatorics package