On the restriction of cross characteristic representations of 2 F 4(q) to proper subgroups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

On the restriction of cross characteristic representations of 2 F 4(q) to proper subgroups

Authors:	Frank Himstedt Hung Ngoc Nguyen Pham Huu Tiep

Affiliation:	1. Zentrum Mathematik, SB-S-MA, Technische Universit?t München, Boltzmannstr. 3, 85748, Garching, Germany 2. Department of Mathematics, Michigan State University, East Lansing, MI, 48824, USA 3. Department of Mathematics, University of Arizona, Tucson, AZ, 85721, USA

Abstract:	We prove that the restriction of any nontrivial representation of the Ree groups ² F ₄(q), q = 2²ⁿ⁺¹ ≥ 8 in odd characteristic to any proper subgroup is reducible. We also determine all triples (K, V, H) such that ${K in {^2F_4(2), ^2F_4(2)'} }We prove that the restriction of any nontrivial representation of the Ree groups ² F ₄(q), q = 2²ⁿ⁺¹ ≥ 8 in odd characteristic to any proper subgroup is reducible. We also determine all triples (K, V, H) such that K ? {²F₄(2), ²F₄(2)￠}{K in {^2F_4(2), ^2F_4(2)'} } , H is a proper subgroup of K, and V is a representation of K in odd characteristic restricting absolutely irreducibly to H.

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