Character degrees and random walks in finite groups of Lie type

• Autores: Martin W. Liebeck, Aner Shalev
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 90, Nº 1, 2005, págs. 61-86
• Idioma: inglés
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• Resumen

  • For a finite group $H$, let $Irr(H)$ denote the set of irreducible characters of $H$, and define the ¿zeta function¿ $\zeta^H(t) = \sum_{\chi \in Irr(H)} \chi(1)^{-t}$ for real $t > 0$. We study the asymptotic behaviour of $\zeta^H(t)$ for finite simple groups $H$ of Lie type, and also of a corresponding zeta function defined in terms of conjugacy classes. Applications are given to the study of random walks on simple groups, and on base sizes of primitive permutation groups.