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SYMF::SfInternal -- computes the inner tensor product of symmetric functions

Call(s)


SYMF::SfInternal(sf1, sf2)

Parameters

sf1, sf2 = any symmetric functions

Introduction

The SYMF::SfInternal function computes the inner tensor product of symmetric functions sf1 and sf2. This operation is also called the internal product. Since sf1 and sf2 may be seen as virtual characters, SYMF::SfInternal computes the symmetric function associated with the product (Kronecker product) of these two virtual characters.

For the basis of products of power-sums, SYMF::SfInternal(p[part], p[part']) = 0 if part<>part', = SfZee(part) x p[part] otherwise.

The result is expressed in the product of power-sums basis.

Example 1

>> muEC::SYMF::SfInternal( p[3,3,2,1,1], p[3,3,2,1,1] );
                            72 p[3, 3, 2, 1, 1]
>> muEC::SYMF::SfZee( [3,3,2,1,1] );
                                    72
>> muEC::SYMF::SfInternal( s[3,2,1], p[3]*h[3] );
                          2 p[3, 3]   p[3, 1, 1, 1]
                        - --------- - -------------
                              3             3

Related Functions

Char2Sf, SfPlethysm, Sf2Char, SfZee

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MuPAD Combinat, an open source algebraic combinatorics package