Reducibility modulo p of complex representations of finite groups of lie type: Asymptotical result and small characteristic cases

Pham Huu Tiep, A. E. Zalesskii

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Abstract

Let G be a finite group of Lie type in characteristic p. This paper addresses the problem of describing the irreducible complex (or p-adic) representations of G that remain absolutely irreducible under the Brauer reduction modulo p. An efficient approach to solve this problem for p > 3 has been elaborated in earlier papers by the authors. In this paper, we use arithmetical properties of character degrees to solve this problem for the groups G ∈ {2B2(q), 2G2(q), G2(q), 2F4(q), F4(q), 3D4(q)} provided that p ≤ 3. We also prove an asymptotical result, which solves the problem for all finite groups of Lie type over double-struck F signq with q large enough.

Original languageEnglish (US)
Pages (from-to)3177-3184
Number of pages8
JournalProceedings of the American Mathematical Society
Volume130
Issue number11
DOIs
Publication statusPublished - Nov 1 2002
Externally publishedYes

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Keywords

  • Finite groups of Lie type
  • Reduction modulo p
  • Steinberg representation

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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