Linear representation theory of general linear group over a finite field

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