Quantum linear groups and representations of GLn (Fq).

Intro -- Contents -- Introduction -- 1 Quantum linear groups and polynomial induction -- 1.1 Symmetric groups and Hecke algebras -- 1.2 The g-Schur algebra -- 1.3 Tensor products and Levi subalgebras -- 1.4 Polynomial induction -- 1.5 Schur algebra induction -- 2 Classical results on GL[sub(n)] -- 2.1 Conjugacy classes and Levi subgroups -- 2.2 Harish-Chandra induction and restriction -- 2.3 Characters and Deligne-Lusztig operators -- 2.4 Cuspidal representations and blocks -- 2.5 Howlett-Lehrer theory and the Gelfand-Graev representation -- 3 Connecting GL[sub(n)] with quantum linear groups -- 3.1 Schur functors -- 3.2 The cuspidal algebra -- 3.3 'Symmetric' and 'exterior' powers -- 3.4 Endomorphism algebras -- 3.5 Standard modules -- 4 Further connections and applications -- 4.1 Base change -- 4.2 Connecting Harish-Chandra induction with tensor products -- 4.3 p-Singular classes -- 4.4 Blocks and decomposition numbers -- 4.5 The Ringel dual of the cuspidal algebra -- 5 The affine general linear group -- 5.1 Levels and the branching rule from AGL[sub(n)] to GL[sub(n)] -- 5.2 Affine induction operators -- 5.3 The affine cuspidal algebra -- 5.4 The branching rule from GL[sub(n)] to AGL[sub(n-1) -- 5.5 A dimension formula for irreducibles -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.