On the restriction of cross characteristic representations of ²F₄(q) to proper subgroups

2009/10/25 by Frank Himstedt, Hung Ngoc Nguyen, Himstedt, Frank +3
Computer Science · Mathematics · #Advanced Algebra and Geometry #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT

paper · pdf · doi:10.48550/arxiv.0910.4758

9 pages. Arch. d. Math, to appear

arxiv created 2009/10/25 · openalex publication_date 2009/10/25 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that the restriction of any nontrivial representation of the Ree groups ²F₄(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)'\, 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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