The complex linear representations of GL(2, k), k a finite field

  • Luisa Aburto-Hageman Pontificia Universidad Católica de Valparaíso.
  • Roberto Johnson Pontificia Universidad Católica de Valparaíso.
  • José Pantoja Pontificia Universidad Católica de Valparaíso.
Palabras clave: Complex linear representations, finite groups, theory of group representations, representaciones lineales complejas, grupos finitos, teoría de representaciones de grupos.

Resumen

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.

Biografía del autor

Luisa Aburto-Hageman, Pontificia Universidad Católica de Valparaíso.
Instituto de Matemáticas.
Roberto Johnson, Pontificia Universidad Católica de Valparaíso.
Instituto de Matemáticas.
José Pantoja, Pontificia Universidad Católica de Valparaíso.
Instituto de Matemáticas.

Citas

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Publicado
2017-05-08
Cómo citar
Aburto-Hageman, L., Johnson, R., & Pantoja, J. (2017). The complex linear representations of GL(2, k), k a finite field. Proyecciones. Revista De Matemática, 25(3), 307-329. https://doi.org/10.4067/S0716-09172006000300007
Sección
Artículos