Resolutions of \(B\) modules

DOI10.1016/0019-3577(94)90003-5zbMath0821.20026OpenAlexW2038192736MaRDI QIDQ1344158

Stephen R. Doty

Publication date: 6 March 1995

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0019-3577(94)90003-5

zbMATH Keywords

general linear groupsdualityhighest weight categoryVerma modulesinductionirreducible polynomial representationsBorel subgroupsWeyl character formulaminimal injective resolutionBGG resolutionscategory of rational \(B\)- modulesDonkin truncationJacobi-Trudi expansionminimal injective rational \(B\)-modulesminimal injective rational modules

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Representation theory for linear algebraic groups (20G05) Homological methods in Lie (super)algebras (17B55) Resolutions; derived functors (category-theoretic aspects) (18G10) Cohomology theory for linear algebraic groups (20G10)

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Cites Work

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• On Schur algebras and related algebras. I
• On Schur algebras and related algebras. II
• Resolutions, dual pairs, and character formulas
• Longest weight vectors and excellent filtrations
• On complexes relating the Jacobi-Trudy identity with the Bernstein- Gelfand-Gelfand resolution
• Cohomology, hyperalgebras, and representations
• Polynomial representations of \(GL_n\)
• Modular symmetric functions and irreducible modular representations of general linear groups
• Locally finite representations
• A vanishing theorem for Schur modules
• Lie algebra cohomology and the generalized Borel-Weil theorem
• A note on decomposition numbers for general linear groups and symmetric groups
• Introduction to Lie Algebras and Representation Theory