Source algebra equivalences for blocks¶of finite general linear groups over a fixed field
Copyright policy )Source algebra equivalences for blocks¶of finite general linear groups over a fixed field
Let \(q\) be a prime power, let \(p\) be a prime not dividing \(q\), and let \(D\) be a finite \(p\)-group. The author shows that the source algebras of unipotent \(p\)-blocks of \(\text{GL}(n,q)\) with defect group \(D\), as \(n\) varies, fall into finitely many isomorphism classes. This establishes a special case of a general conjecture of Puig and extends earlier results of \textit{T. Jost} [Manuscr. Math. 91, No. 1, 121-144 (1996; Zbl 0896.20009)] on a conjecture of Donovan. The proof makes use of \textit{L. Puig}'s refinement [Algebra Colloq. 1, No. 1, 25-55 (1994; Zbl 0830.20024)] of methods introduced by \textit{J. Scopes} [J. Algebra 142, No. 2, 441-455 (1991; Zbl 0736.20008)].
- University of Manchester United Kingdom
- University of Manchester United Kingdom
- Walbrook Institute London United Kingdom
Representation theory for linear algebraic groups, Modular representations and characters, Donovan conjecture, Representations of finite groups of Lie type, source algebras, Linear algebraic groups over finite fields, blocks, Puig conjecture, defect groups, Group rings of finite groups and their modules (group-theoretic aspects)
Representation theory for linear algebraic groups, Modular representations and characters, Donovan conjecture, Representations of finite groups of Lie type, source algebras, Linear algebraic groups over finite fields, blocks, Puig conjecture, defect groups, Group rings of finite groups and their modules (group-theoretic aspects)
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