Modular Harish-Chandra series, Hecke algebras and (generalized) \(q\)-Schur algebras (Q2776256)

This paper deals with the connections between the representations of finite groups of Lie type in non-defining characteristic and representations of Hecke algebras and (generic) \(q\)-Schur algebras. The aim of this paper is to describe the conditions and the concepts underlying the strategy of reducing the problem of finding decomposition numbers of finite groups of Lie type to a similar problem about generalized \(q\)-Schur algebras. These concepts include (1) Hom functors, (2) Harish-Chandra philosophy, (3) Decomposition numbers and Brauer reciprocity.NEWLINENEWLINEFor the entire collection see [Zbl 0977.00027].