Towards a Jordan decomposition of blocks of finite reductive groups

2013/11/30 by Michel Enguehard, Michel E. Enguehard, Enguehard, Michel E. · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #math.GR

paper · pdf · doi:10.48550/arxiv.1312.0106

arxiv created 2013/11/30 · openalex publication_date 2013/11/30 · arxiv updated 2013/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

\input amssym.def \input amssym.tex Let G be a connected algebraic reductive group over an algebraic closure of a prime field \Bbb F_p, defined over \Bbb F_q thanks to a Frobenius F. Let ℓ be a prime different from p. Let B be an ℓ-block of the subgroup of rational points G^F. Under mild restrictions on ℓ, we show the existence of an algebraic reductive group H defined over \Bbb F_q \it via a Frobenius F, and of a unipotent ℓ-block b of H^F such that : the respective defect groups of b and B are isomorphic, the associated Brauer categories are isomorphic and there is a height preserving one-to-one map from the set of irreducible representations of b onto the set of irreducible representations of B. \end

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