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

## Contents

This article gives specific information, namely, linear representation theory, about a family of groups, namely: special linear group. This article restricts attention to the case where the underlying ring is a finite field.
View linear representation theory of group families | View other specific information about special linear group | View other specific information about group families for rings of the type finite field

## Particular cases

### Particular cases by degre

Value of degree $n$ Linear representation theory of
special linear group $SL(n,q)$
order of group Degree as a polynomial in $q$ (= $n^2 - 1$) Number of irreducible representations equals number of conjugacy classes (see number of conjugacy classes in special linear group of fixed degree over a finite field is PORC function of field size)
1 it is the trivial group 1 0 1
2 link $q^3 - q$ 3 $q + 1$ if $q$ even $q + 4$ if $q$ odd
3 link $q^3(q^3 - 1)(q^2 - 1)$ 8 $q(q + 1)$ if $q$ not 1 mod 3 $q^2 + q + 8$ if $q$ is 1 mod 3
4 link $q^6(q^4 - 1)(q^3 - 1)(q^2 - 1)$ 15 $q^3 + q^2 + q$ if $q$ even $q^3 + q^2 + 4q + 3$ if $q$ is 3 mod 4 $q^3 + q^2 + 4q + 15$ if $q$ is 1 mod 4