nLab pseudovector representation

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) $\mathbf{1}_{{}_{sgn}}$:

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

Related concepts

• vector representation

• pseudoscalar, density

• pseudovector meson