TY - JOUR

T1 - Reducibility modulo p of complex representations of finite groups of lie type

T2 - Asymptotical result and small characteristic cases

AU - Tiep, Pham Huu

AU - Zalesskii, A. E.

N1 - Copyright:
Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.

PY - 2002/11/1

Y1 - 2002/11/1

N2 - 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.

AB - 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.

KW - Finite groups of Lie type

KW - Reduction modulo p

KW - Steinberg representation

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U2 - 10.1090/S0002-9939-02-06459-6

DO - 10.1090/S0002-9939-02-06459-6

M3 - Article

AN - SCOPUS:0036842544

VL - 130

SP - 3177

EP - 3184

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 11

ER -