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

• Aburto-Hageman, Luisa ^[1] ; Johnson, Roberto ^[1] ; Pantoja, José ^[1]
  1. [1] Pontificia Universidad Católica de Valparaíso

     Pontificia Universidad Católica de Valparaíso

     Valparaíso, Chile

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 25, Nº. 3, 2006, págs. 307-329
• Idioma: inglés
• DOI: 10.4067/S0716-09172006000300007
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• 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.

• Referencias bibliográficas
  • Citas [A] L. Aburto, Green’s Formulas for SL2(k), Communications in Algebra, 24 (11), pp. 3489-3499, (1996).
  • [Cu-Re] C. Curtis and I. Reiner, Representation Theory of Finite Groups and Associative Algebras, Willey, N. York, (1962).
  • [G] S. Gelfand, Representations of the General Linear Group over a Finite Field, Mat. Sb. 83 1970, pp. 15-41, (1970).
  • [PS] I. Piatetski-Shapiro, Complex Representations of GL(2, k) for Finite Fields k, Contemporary Mathematics, Volume 16, AMS, (1983).
  • [S] K. Spindler, Abstract Algebra with Applications, Dekker, (1994).
  • [SA1] J. Soto-Andrade, Métodos Geométricos en Teoría de Representaciones de Grupos Finitos, IX Escuela Latinoamericana de Matemáticas (ELAM),...
  • [SA2] J. Soto-Andrade, Représentations de Certain Groupes Symplectiques Finis, Bull. Soc. Math. France, pp. 5-334, (1978).
  • [Se] J.P. Serre, Linear Representations of Finite Groups, SpringerVerlag, (1977)
  • [T] A. Terras, Fourier Analysis on Finite Groups and Applications, L. M. S. 43, Cambridge University Press, (2001).