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.
The object GroupActing is a symbol.