FUNCTION: SfOmega - apply the omega-automorphism

CALLING SEQUENCE:

SfOmega(sf)

SYMF[SfOmega](sf)

PARAMETERS:

sf = any symmetric function

SYNOPSIS:

• The SfOmega function applies the omega-automorphism to the symmetric function sf. This involution is defined as: h.i -> e.i, e.i -> h.i and p.i -> (-1)^(i-1) p.i. In terms of Schur functions, the involution conjugates the indexing partition.

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

EXAMPLES:

> with(SYMF):
> SfOmega(h3);
 
                                       e3
 
> SfOmega(p4);
 
                                      - p4