Proyecciones
Vol. 25, No 3, pp. 307-329, December 2006.
Universidad Católica del Norte
Antofagasta - Chile

THE COMPLEX LINEAR REPRESENTATIONS OF GL(2, k), k A FINITE FIELD

LUISA ABURTO^*, ROBERTO JOHNSON ^†‡, JOSÉ PANTOJA ^§¶

P. UNIVERSIDAD CATÓLICA DE VALPARAÍSO, CHILE

Abstract

Let k be a finite field of odd characteristic, and let G be the group of all invertible 2 ¡¿ 2 matrices over k. We construct the irreducible complex linear representations of the group G.The constructions lean on the method of induction from subgroups and on the theory of characters. To accomplish this goal, the basic facts from the theory of representations and characters of finite groups are presented. Furthermore, we describe the structure of G that we need, and the theory of representations of some subgroups of G that we use. As a final result, we obtain the theory of the irreducible representations of G,by describing either the irreducible representations of , or the irreducible characters of the group G.

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Luisa Aburto-Hageman
Instituto de Matemáticas
Pontificia Universidad Católica de Valparaíso
Casilla 4059
Valparaíso
CHILE
email: laburto@ucv.cl

Roberto Johnson
Instituto de Matemáticas
Pontificia Universidad Católica de Valparaíso
Casilla 4059
Valparaíso
CHILE
email: rjohnson@ucv.cl

and

José Pantoja
Instituto de Matemáticas
Pontificia Universidad Católica de Valparaíso
Casilla 4059
Valparaíso
CHILE
email: jpantoja@ucv.cl

Received : October 2006. Accepted : November 2006

Partially supported by Pontificia Universidad Católica de Valparaíso DI 124.709/2006

^†Partially supported by Pontificia Universidad Católica de Valparaíso DI 124.708/2006
^‡Partially supported by Universidad Católica del Norte, as a visiting professor
^§Partially supported by FONDECYT 106051 and P. Universidad Católica de Valparaiso
^¶Partially supported by Universidad Católica del Norte, as a visiting professor