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 a symbol.