nLab vector representation



Representation theory

representation theory

geometric representation theory


representation, 2-representation, ∞-representation

Geometric representation theory

Representation theory

Spin geometry



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 13:02:04. See the history of this page for a list of all contributions to it.