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## `SFA::SfAOmega` -- applies the Omega-automorphism

#### Call(s)

`SFA::SfAOmega(sfa <,alist>)`

#### Parameters

`sfa` | - | any symmetric function
`alist` | - | a list of alphabets

#### Introduction

The `SFA::SfAOmega` function applies the Omega-automorphism to the symmetric function `sfa`.

This involution is defined as:

              h[i](A) ->> e[i](A),
              e[i](A) ->> h[i](A),
              p[i](A) ->> (-1)^(i-1) p[i](A).

In terms of Schur functions, the involution conjugates the indexing partition.

One can apply `SFA::SfAOmega` solely on symmetric functions over the alphabets given in the second parameter `alist`.

#### Example 1

    >> muEC::SFA::SfAOmega( p[3,1](A1) - q*s[3](A2) );

                          p[3, 1](A1) - q s[1, 1, 1](A2)

    >> muEC::SFA::SfAOmega( p[3,1](A1) - q*s[3](A2), [ A1 ]);

                             p[3, 1](A1) - q s[3](A2)

#### Related Functions

`SYMF::SfOmega`, `PART::Part2Conjugate`

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MuPAD Combinat, an open source algebraic combinatorics package