On the restriction of cross characteristic representations of 2 F 4(q) to proper subgroups |
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Authors: | Frank Himstedt Hung Ngoc Nguyen Pham Huu Tiep |
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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
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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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