Operations on Group Representations

Intersection(V, W): ModRed, ModRed -> ModRed

V meet W: ModRed, ModRed -> ModRed

If \(V, W \subseteq U\) are both subrepresentations of \(U\), return the intersection \(V \cap W \subseteq U\).

V eq W: ModRed, ModRed -> BoolElt

V eq W: CombFreeMod, CombFreeMod -> BoolElt

Returns true if the representations \(V\) and \(W\) are equal; otherwise false

Base Change

ChangeRing(V, S): ModRed, Rng -> ModRed

The group representation \(V_S = V \otimes_R S\) with base ring changed to \(S\).

ChangeRing(M, S): CombFreeMod, Rng -> CombFreeMod

The module \(M_S = M \otimes_R S\) with base ring changed to \(S\).

Other Operations

FixedSubspace(H, V): GrpMat, ModRed -> ModRed

Given a subgroup \(H \subseteq G\), returns the subspace \(V^H\), the vectors of \(V\) fixed by \(H\).