On the determinant of Shapovalov form for generalized Verma modules

DOI10.1006/jabr.1998.7731zbMath0931.17004OpenAlexW2048041575MaRDI QIDQ1291112

Alexandre Khomenko, Volodymyr Mazorchuk

Publication date: 27 February 2000

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

Full work available at URL: https://doi.org/10.1006/jabr.1998.7731

zbMATH Keywords

enveloping algebraShapovalov form\(\alpha\)-stratified generalized Verma modulesBGG theoremcontragradient Lie algebra

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Universal enveloping (super)algebras (17B35)

Related Items (4)

An admissible level \(\widehat{\mathfrak{osp}}(1| 2)\)-model: modular transformations and the Verlinde formula ⋮ Yetter-Drinfeld modules over Nichols systems: reflections, induced objects and maximal subobject ⋮ Differential equations in vertex algebras and simple modules for the Lie algebra of vector fields on a torus ⋮ Generalized Verma modules induced from \(sl(2,\mathbb{C})\) and associated Verma modules

Cites Work

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• Infinite dimensional Lie algebras. An introduction
• Submodule structure of generalized Verma modules induced from generic Gelfand-Zetlin modules
• Structure of representations with highest weight of infinite-dimensional Lie algebras
• Stratified \(L\)-modules
• On a bilinear form on the universal enveloping algebra of a complex semisimple Lie algebra
• Irreducible non-dense \(A_ 1^{(1)}\)-modules
• Structure of \(\alpha\)-stratified modules for finite-dimensional Lie algebras. I
• Structure of representations generated by vectors of highest weight
• Generalized verma modules over the lie algebra of typeG₂

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