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 \({K \in \{^2F_4(2), ^2F_4(2)'\} }\) , 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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Part of this work was done while the authors were participating in the program on Representation Theory of Finite Groups and Related Topics at the Mathematical Sciences Research Institute (MSRI), Berkeley. It is a pleasure to thank the organizers Professors J. L. Alperin, M. Broué, J. F. Carlson, A. S. Kleshchev, J. Rickard, B. Srinivasan for generous hospitality and support and stimulating environment.
P. H. Tiep gratefully acknowledges the support of the NSF (grants DMS-0600967 and DMS-0901241).
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Himstedt, F., Nguyen, H.N. & Tiep, P.H. On the restriction of cross characteristic representations of 2 F 4(q) to proper subgroups. Arch. Math. 93, 415–423 (2009). https://doi.org/10.1007/s00013-009-0051-2
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DOI: https://doi.org/10.1007/s00013-009-0051-2