Generic and \(q\)-rational representation theory

DOI10.2977/prims/1195144189zbMath0998.20017OpenAlexW2094651084MaRDI QIDQ1974442

Brian J. Parshall, Leonard L. Scott, Edward Cline

Publication date: 25 August 2002

Published in: Publications of the Research Institute for Mathematical Sciences, Kyoto University (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2977/prims/1195144189

zbMATH Keywords

ordersgeneral linear groupsMorita equivalencescohomology groupsderived equivalences\(q\)-Schur algebrasprojective resolutionsBrauer charactersquasi-hereditary algebrasdecomposition numbersmodular representationsgeneric propertiessemisimple algebrasnon-describing characteristic

Mathematics Subject Classification ID

Linear algebraic groups over finite fields (20G40) Representations of orders, lattices, algebras over commutative rings (16G30) Representation theory for linear algebraic groups (20G05) Modular representations and characters (20C20) Representations of finite groups of Lie type (20C33) Cohomology theory for linear algebraic groups (20G10)

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Cites Work

• On the cohomology of algebraic and related finite groups
• Integral and graded quasi-hereditary algebras. I
• Cohomology of infinitesimal and discrete groups
• A \(q\)-analogue of \(U(\mathfrak{gl}(N+1))\), Hecke algebra, and the Yang-Baxter equation
• On some geometric aspects of Bruhat orderings. II: The parabolic analogue of Kazhdan-Lusztig polynomials
• Quasi-hereditary algebras
• Representations of Coxeter groups and Hecke algebras
• Modular Harish-Chandra theory. I
• Rational and generic cohomology
• Twisted homological stability for general linear groups
• Cohomology of finite groups of Lie type. I
• Stratifying endomorphism algebras associated to Hecke algebras
• On quotients of Hom-functors and representations of finite general linear groups. II
• Quantum Weyl reciprocity and tilting modules
• On tilting modules for algebraic groups
• A \(q\)-analogue of the Coxeter complex
• Some generic representations, \(W\)-graphs, and duality
• Cells and \(q\)-Schur algebras
• Kazhdan-Lusztig conjecture for affine Lie algebras with negative level
• The group ring of \(\text{GL}_ n(q)\) and the \(q\)-Schur algebra
• Characteristic-free representation theory of the general linear group. II: Homological considerations
• The blocks of finite general linear and unitary groups
• The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences
• Decomposition numbers of finite classical groups for linear primes.
• Tensor Structures Arising from Affine Lie Algebras. I
• The Characters of the Finite General Linear Groups
• Two-Parameter Quantum Linear Groups and the Hyperbolic Invariance of q -Schur Algebras
• On the Decomposition Numbers of the Finite General Linear Groups
• Representations of Hecke Algebras of General Linear Groups
• Morita Theory for Derived Categories
• q-Tensor Space and q-Weyl Modules
• The Homological Dual of a Highest Weight Category
• Lusztig conjectures, old and new, I.
• KOSZUL ALGEBRAS AND THE FROBENIUS AUTOMORPHISM
• Koszul Duality Patterns in Representation Theory
• Quantum linear groups
• Maximal subgroups of finite groups
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