Category \(\mathcal O\) for quantum groups

DOI10.4171/JEMS/506zbMath1393.17025arXiv1105.5500OpenAlexW1671809287MaRDI QIDQ2019200

Volodymyr Mazorchuk, Henning Haahr Andersen

Publication date: 27 March 2015

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.5500

zbMATH Keywords

tilting modulescategory \(\mathcal{O}\)quantized enveloping algebras

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37) Representation theory for linear algebraic groups (20G05)

Related Items (19)

BGG categories in prime characteristics ⋮ Highest weight 𝔰𝔩₂-categorifications II: Structure theory ⋮ Cellular structures using \(U_q\)-tilting modules ⋮ On projective modules in category \(\mathcal{O}_{\text{int}}\) of quantum \(\mathfrak{sl}_{2}\) ⋮ Tensor products of infinite dimensional modules in the BGG category of a quantized simple Lie algebra of type ADE ⋮ Highest weight modules over the quantum periplectic superalgebra of type \(P\) ⋮ Whittaker categories, properly stratified categories and Fock space categorification for Lie superalgebras ⋮ The relative monoidal center and tensor products of monoidal categories ⋮ Dirac operator and its cohomology for the quantum group Uq(𝖘𝖑𝟐) ⋮ Comodule algebras and 2-cocycles over the (Braided) Drinfeld double ⋮ Tensor product varieties, perverse sheaves, and stability conditions ⋮ Comparison of unitary duals of Drinfeld doubles and complex semisimple Lie groups ⋮ Parabolic category O for classical Lie superalgebras ⋮ 2-Verma modules ⋮ Rigid analytic quantum groups and quantum Arens-Michael envelopes ⋮ Cohomology rings for quantized enveloping algebras ⋮ BGG CATEGORY FOR THE QUANTUM SCHRÖDINGER ALGEBRA ⋮ Braided Drinfeld and Heisenberg doubles. ⋮ SOME HOMOLOGICAL PROPERTIES OF CATEGORY FOR LIE SUPERALGEBRAS

Cites Work

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• Highest weight categories arising from Khovanov's diagram algebra. II: Koszulity
• Kazhdan-Lusztig conjecture and holonomic systems
• Category of \(\mathfrak g\) modules
• Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra \(\mathfrak q(n)\)
• Representations of quantum algebras
• Representations of quantum algebras. The mixed case.
• Injective Modules for Quantum Algebras
• Kazhdan-Lusztig polynomials and character formulae for the Lie superalgebra 𝔤𝔩(𝔪|𝔫)
• Stratifying endomorphism algebras

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