nLab
vector representation

Contents

Context

Representation theory

representation theory

geometric representation theory

Ingredients

Definitions

representation, 2-representation, ∞-representation

Geometric representation theory

Theorems

Representation theory

Spin geometry

Contents

Definition

Let GSpin(V)πSO(V)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)Spin(V) is called the vector representation if it comes via π\pi from the defining linear representation of SO(V)SO(V) on the vector space underlying the given inner product space VV.

Last revised on April 6, 2020 at 09:02:04. See the history of this page for a list of all contributions to it.