On quotients of Hom-functors and representations of finite general linear groups. I

DOI10.1016/0021-8693(90)90111-ZzbMath0698.20005MaRDI QIDQ912205

Richard Dipper

Publication date: 1990

Published in: Journal of Algebra (Search for Journal in Brave)

zbMATH Keywords

general linear groupsorderdecomposition matricessemisimple algebramodular representationmodule categoriesfinitely generated T-modules

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Representation theory for linear algebraic groups (20G05) Modular representations and characters (20C20) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05)

Related Items (18)

The Brauer trees of the exceptional Chevalley groups of type \(E_ 6\) ⋮ The number of trivial composition factors of the Steinberg module ⋮ On the 2-decomposition numbers of Steinberg's triality groups \(^3D_4(q)\), \(q\) odd. ⋮ Decomposition matrices for exceptional groups at \(d=4\) ⋮ On the decomposition numbers of the Ree groups \(^2F_4(q^2)\) in non-defining characteristic. ⋮ Brauer trees of unipotent blocks ⋮ 3-blocks and 3-modular characters of \(G_ 2(q)\) ⋮ Smooth representations modulo \(\ell\) of \(\mathrm{GL}_m(D)\) ⋮ Projective simple modules of symmetric algebras and their specializations with applications to Hecke algebras ⋮ Representations of Hecke algebras of type \(B_n\) ⋮ Schur subalgebras and an application to the symmetric group ⋮ Modular Harish-Chandra theory. I ⋮ Rouquier blocks in Chevalley groups of type \(E\). ⋮ On the Decomposition Numbers of Steinberg's Triality Groups³D₄(2ⁿ) in Odd Characteristics ⋮ Branching Rules for General Linear Groups ⋮ On quotients of Hom-functors and representations of finite general linear groups. II ⋮ Modular Harish-Chandra theory. II ⋮ On the center of affine Hecke algebras of type \(A\).

Cites Work

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• Identification of the irreducible modular representations of \(GL_n(q)\).
• Representations of finite Chevalley groups. A survey
• Polynomial representations of \(GL_n\)
• Unipotent representations of the finite general linear groups
• Modules with decompositions that complement direct summands
• The Characters of the Finite General Linear Groups
• The q ‐Schur Algebra
• On the Decomposition Numbers of the Finite General Linear Groups
• On the Decomposition Numbers of the Finite General Linear Groups. II
• The Irreducible Representations of the Finite General Linear Groups
• Representation Theory of Artin Algebras I
• Representation Theory of Artin Algebras II

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