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

Frank Himstedt; Hung Ngoc Nguyen; Pham Huu Tiep

doi:10.1007/s00013-009-0051-2

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

Frank Himstedt, Hung Ngoc Nguyen, Pham Huu Tiep

Mathematics

Research output: Contribution to journal › Article › peer-review

3 Scopus citations

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 ε {²F₄(2), ²F₄(2)′}, H is a proper subgroup of K, and V is a representation of K in odd characteristic restricting absolutely irreducibly to H.

Original language	English (US)
Pages (from-to)	415-423
Number of pages	9
Journal	Archiv der Mathematik
Volume	93
Issue number	5
DOIs	https://doi.org/10.1007/s00013-009-0051-2
State	Published - Nov 2009

Keywords

Cross characteristic representations
Irreducible restrictions

ASJC Scopus subject areas

General Mathematics

Access to Document

10.1007/s00013-009-0051-2

Cite this

@article{048e0bfb7402487b8c9763bbfb354042,

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

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 ε {2F4(2), 2F4(2)′}, H is a proper subgroup of K, and V is a representation of K in odd characteristic restricting absolutely irreducibly to H.",

keywords = "Cross characteristic representations, Irreducible restrictions",

author = "Frank Himstedt and Nguyen, {Hung Ngoc} and Tiep, {Pham Huu}",

note = "Funding Information: 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. Brou{\'e}, 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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doi = "10.1007/s00013-009-0051-2",

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T1 - On the restriction of cross characteristic representations of 2 F 4(q) to proper subgroups

AU - Himstedt, Frank

AU - Nguyen, Hung Ngoc

AU - Tiep, Pham Huu

N1 - Funding Information: 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).

PY - 2009/11

Y1 - 2009/11

N2 - 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 ε {2F4(2), 2F4(2)′}, H is a proper subgroup of K, and V is a representation of K in odd characteristic restricting absolutely irreducibly to H.

AB - 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 ε {2F4(2), 2F4(2)′}, H is a proper subgroup of K, and V is a representation of K in odd characteristic restricting absolutely irreducibly to H.

KW - Cross characteristic representations

KW - Irreducible restrictions

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U2 - 10.1007/s00013-009-0051-2

DO - 10.1007/s00013-009-0051-2

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