Counting p'-characters in finite reductive groups

• Autores: Olivier Brunat
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 81, Nº 3, 2010, págs. 544-562
• Idioma: inglés
• DOI: 10.1112/jlms/jdq001
• Enlaces
  • Texto completo (pdf)
• Resumen

  • This article is concerned with the relative McKay conjecture for finite reductive groups. Let G be a connected reductive group defined over the finite field Fq of characteristic p > 0 with corresponding Frobenius map F. We prove that, if p is a good prime for G and if the group of F-coinvariants of the component group of the centre of G has prime order, then the relative McKay conjecture holds for GF at the prime p. In particular, this conjecture is true for GF in the defining characteristic for a simple simply connected group G of type Bn, Cn, E6 or E7.

    Our main tools are the theory of Gelfand�Graev characters for connected reductive groups with disconnected centre developed by Digne, Lehrer and Michel and the theory of cuspidal Levi subgroups. We also explicitly compute the number of semisimple classes of GF for any simple algebraic group G.