nLab vector representation

Definition

Let $G \coloneqq Spin(V) \overset{\pi}{\to} SO(V)$ be a spin group extension of a special orthogonal group, or more generally a Pin group-extension of an orthogonal group (or Lorentz group, …).

Then a spin representation of $Spin(V)$ is called the vector representation if it comes via $\pi$ from the defining linear representation of $SO(V)$ on the vector space underlying the given inner product space $V$.

Related concepts

• real spin representation

• pseudovector representation

• vector meson