# GroupActing -- Specifies the group that is acting

## Description

This is an optional argument for the schurRing and symmetricRing functions. When the exterior or symmetric powers of a symmetric function g are computed, the result depends on whether g is interpreted as a virtual representation of a general linear or symmetric group. The option GroupActing specifies the interpretation to be considered. Its possible values are "GL" and "Sn", with the former being the default.

 i1 : S = schurRing(s,2); i2 : exteriorPower(3,s_2) o2 = s 3,3 o2 : S i3 : T = schurRing(t,2,GroupActing => "Sn"); i4 : symmetricPower(2,t_{1,1}) o4 = t 2 o4 : T

The first example computes the decomposition of \Lambda^3(Sym^2(V)) into irreducible GL(V)-representations, while the second one computes the second symmetric power of the sign representation of the symmetric group S_2.

## Functions with optional argument named GroupActing :

• "schurRing(...,GroupActing=>...)"
• "symmetricRing(...,GroupActing=>...)"

## For the programmer

The object GroupActing is .