# Linear representation theory of general linear group over a finite field

## Contents

This article gives specific information, namely, linear representation theory, about a family of groups, namely: general linear group.
View linear representation theory of group families | View other specific information about general linear group

This article describes the linear representation theory of the general linear group of finite degree over a finite field, i.e., a group of the form $GL(n,\mathbb{F}_q)$, also denoted $GL(n,q)$, defined as the general linear group of degree $n$ over the (unique up to isomorphism) field of size $q$.

## Particular cases

### Particular cases by degree

Value of degree $n$ Linear representation theory of special linear group $SL(n,q)$
1 the general linear group is a cyclic group of size $q - 1$, given by the multiplicative group of $\mathbb{F}_q$ -- see multiplicative group of a finite field is cyclic and linear representation theory of finite cyclic groups
2 linear representation theory of general linear group of degree two over a finite field
3 linear representation theory of general linear group of degree three over a finite field