Cohomology and Ext for rank one finite groups of Lie type in cross characteristic

2022/08/25 by Jack Saunders, Saunders, Jack
Mathematics · #20C20 (Primary) #20C33 (Secondary) #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2208.11937

openalex publication_date 2022/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the dimensions of Ext_Gⁿ(V, W) for all irreducible V, W lying in r-blocks of cyclic defect in the simple groups Sz(q), PSU₃(q) and \operatorname²G₂(q) in cross characteristic, obtaining in particular the dimensions of all cohomology groups for such modules. Along the way, we also obtain an analogous result for any r-block of cyclic defect whose Brauer tree is either a star or line (open polygon).

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