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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