Linear representation theory of special linear group over a finite field

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