Singular blocks of parabolic category \(\mathcal O\) and finite \(W\)-algebras

DOI10.1016/j.jpaa.2011.03.020zbMath1295.17009arXiv0909.1860OpenAlexW1532608626MaRDI QIDQ649842

Ben Webster

Publication date: 6 December 2011

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.1860

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Universal enveloping (super)algebras (17B35) Simple, semisimple, reductive (super)algebras (17B20)

Related Items (10)

Semi-infinite cohomology and the linkage principle for \(\mathcal{W}\)-algebras ⋮ Tensor product algebras, Grassmannians and Khovanov homology ⋮ Singular localization of \(\mathfrak{g}\)-modules and applications to representation theory ⋮ Localization for affine \(\mathcal{W} \)-algebras ⋮ Whittaker categories, properly stratified categories and Fock space categorification for Lie superalgebras ⋮ Kostant's problem for Whittaker modules ⋮ Poisson-de Rham homology of hypertoric varieties and nilpotent cones ⋮ The big projective module as a nearby cycles sheaf ⋮ A quantum Mirković-Vybornov isomorphism ⋮ Highest weights for truncated shifted Yangians and product monomial crystals

Cites Work

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• Hypertoric category \(\mathcal O\).
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• Symmetric functions, parabolic category \(\mathcal O\), and the Springer fiber.
• On Whittaker vectors and representation theory
• The composition series of modules induced from Whittaker modules
• Differential operators on homogeneous spaces. I: Irreducibility of the associated variety for annihilators of induced modules
• Special transverse slices and their enveloping algebras
• Some results about geometric Whittaker model.
• Enveloping algebras of Slodowy slices and the Joseph ideal
• Structure of representations generated by vectors of highest weight
• On Koszul duality for Kac-Moody groups
• Parabolic category O, perverse sheaves on Grassmannians, Springer fibres and Khovanov homology
• Highest Weight Theory for Finite W-Algebras
• Harish-Chandra bimodules for quantized Slodowy slices
• Quantized symplectic actions and 𝑊-algebras
• Centers of degenerate cyclotomic Hecke algebras and parabolic category 𝒪
• Categories with projective functors
• Koszul Duality Patterns in Representation Theory
• On the structure of the category O for W-algebras

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