The McKay conjecture and Galois automorphisms

• Autores: Gabriel Navarro Ortega
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 160, Nº 3, 2004, págs. 1129-1140
• Idioma: inglés
• DOI: 10.4007/annals.2004.160.1129
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• Resumen

  • The main problem of representation theory of finite groups is to find proofs of several conjectures stating that certain global invariants of a finite group G can be computed locally. The simplest of these conjectures is the ¿McKay conjecture¿ which asserts that the number of irreducible complex characters of G of degree not divisible by p is the same if computed in a p-Sylow normalizer of G. In this paper, we propose a much stronger version of this conjecture which deals with Galois automorphisms. In fact, the same idea can be applied to the celebrated Alperin and Dade conjectures.