A decomposition theorem for certain self-dual modules in the category \(\mathcal O\)

DOI10.1215/S0012-7094-89-05806-7zbMath0673.17003MaRDI QIDQ1120651

Ronald S. Irving, David H. Collingwood

Publication date: 1989

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

projective modulegeneralized Verma modulessesquilinear formscomplex semisimple Lie algebra}}\) bilinear formscategory \({\mathcal O}{\mathbf{self- dual modules

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Semisimple Lie groups and their representations (22E46) Simple, semisimple, reductive (super)algebras (17B20)

Related Items (18)

On the Relation Between Finitistic and Good Filtration Dimensions ⋮ Tilting Modules for Lie Superalgebras ⋮ Unnamed Item ⋮ Koszul duality for semidirect products and generalized Takiff algebras ⋮ Fusion categories arising from semisimple Lie algebras ⋮ Projective-injective modules, Serre functors and symmetric algebras ⋮ Super duality and Kazhdan-Lusztig polynomials ⋮ Categorification of (induced) cell modules and the rough structure of generalised Verma modules ⋮ Projective functors and the restriction of a Verma module to a subalgebra of Levi type ⋮ Translation and shuffling of projectively presentable modules and a categorification of a parabolic Hecke module ⋮ Multiplicities of second cell tilting modules. ⋮ The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences ⋮ Modules for relative Yangians (family algebras) and Kazhdan-Lusztig polynomials ⋮ Singular blocks of the category \({\mathcal O}\) ⋮ Jacquet modules for semisimple Lie groups having Verma module filtrations ⋮ A combinatorial description of blocks in \({\mathcal O}({\mathcal P},\Lambda)\) associated with \(sl(2)\)-induction ⋮ Character formulas for tilting modules over Kac-Moody algebras ⋮ On tilting modules for algebraic groups

Cites Work

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• Decompositions in categories of highest weight modules
• Splitting Criteria for -Modules Induced from a Parabolic and the Bernstein-Gelfand-Gelfand Resolution of a Finite Dimensional, Irreducible -Module

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