nLab
pseudovector representation

Contents

Contents

Idea

Given a symmetry group GG equipped with a homomorphism GO(V)G \to O(V) to an orthogonal group of some inner product space VV – for instance a Pin group – then its pseudovector representation is the linear representation (over the given ground field kk)

V sgnRep k(G) V_{{}_{sgn}} \;\in\; Rep_k(G)

which is the tensor product of representations of the vector representation VV with the pseudoscalar representation (determinant-representation) 1 sgn\mathbf{1}_{{}_{sgn}}:

V sgnV1 sgn V_{{}_{sgn}} \;\coloneqq\; V \otimes \mathbf{1}_{{}_{sgn}}

Last revised on April 6, 2020 at 09:04:29. See the history of this page for a list of all contributions to it.