Reducibility modulo <IMG > of complex representations of finite groups of Lie type: Asymptotical result and small characteristic cases期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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

Authors:	Pham Huu Tiep A. E. Zalesskii

Affiliation:	Department of Mathematics, University of Florida, Gainesville, Florida 32611-8105 ; School of Mathematics, University of East Anglia, Norwich NR4 7TJ, United Kingdom

Abstract:	Let be a finite group of Lie type in characteristic . This paper addresses the problem of describing the irreducible complex (or -adic) representations of that remain absolutely irreducible under the Brauer reduction modulo . An efficient approach to solve this problem for 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 $begin{displaymath}G in { hspace{0.5mm}^{2}hspace{-0.6mm} B_{2}(q), hspace... ...{4}(q),F_{4}(q), hspace{0.5mm}^{3}hspace{-0.6mm} D_{4}(q)} end{displaymath}$ provided that . We also prove an asymptotical result, which solves the problem for all finite groups of Lie type over ${mathbb F}_{q}$ with large enough.

Keywords:	Finite groups of Lie type reduction modulo $p$ Steinberg representation

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