Linear representation theory of special linear group over a finite field

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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