# nLab vector representation

Contents

### Context

#### Representation theory

representation theory

geometric representation theory

## Theorems

#### Representation theory

representation theory

geometric representation theory

## Spin geometry

spin geometry

Dynkin labelsp. orth. groupspin grouppin groupsemi-spin group
SO(2)Spin(2)Pin(2)
B1SO(3)Spin(3)Pin(3)
D2SO(4)Spin(4)Pin(4)
B2SO(5)Spin(5)Pin(5)
D3SO(6)Spin(6)
B3SO(7)Spin(7)
D4SO(8)Spin(8)SO(8)
B4SO(9)Spin(9)
D5SO(10)Spin(10)
B5SO(11)Spin(11)
D6SO(12)Spin(12)
$\vdots$$\vdots$
D8SO(16)Spin(16)SemiSpin(16)
$\vdots$$\vdots$
D16SO(32)Spin(32)SemiSpin(32)

string geometry

# Contents

## Definition

Let $Spin(V) \overset{\pi}{\to} SO(V)$ be a spin group extension of a special orthogonal 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 $V$.

Created on February 22, 2018 at 05:02:08. See the history of this page for a list of all contributions to it.