# nLab pseudovector representation

Contents

### Context

#### Representation theory

representation theory

geometric representation theory

# Contents

## Idea

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

$V_{{}_{sgn}} \;\in\; Rep_k(G)$

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

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

Last revised on April 6, 2020 at 13:04:29. See the history of this page for a list of all contributions to it.