Singular localization of \(\mathfrak{g}\)-modules and applications to representation theory

DOI10.4171/JEMS/570zbMath1380.17006OpenAlexW2217393665MaRDI QIDQ894192

Kobi Kremnitzer, Erik Backelin

Publication date: 27 November 2015

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

Full work available at URL: https://doi.org/10.4171/jems/570

zbMATH Keywords

Lie algebralocalizationcategory \(\mathcal{O}\)translation functorWhittaker modulesingular block

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Classical groups (algebro-geometric aspects) (14L35)

Related Items (4)

Localization for affine \(\mathcal{W} \)-algebras ⋮ An informal introduction to categorical representation theory and the local geometric Langlands program ⋮ Remarks on the derived center of small quantum groups ⋮ Rational Cherednik algebras and Hilbert schemes

Cites Work

• Representations of semisimple Lie algebras in prime characteristic and the noncommutative Springer resolution
• Singular blocks of parabolic category \(\mathcal O\) and finite \(W\)-algebras
• \(D\)-modules, perverse sheaves, and representation theory. Translated from the Japanese by Kiyoshi Takeuchi
• 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
• Localization of modules for a semisimple Lie algebra in prime characteristic (with an appendix by R. Bezrukavnikov and S. Riche, Computation for \(\text{sl}(3))\)
• Quantum flag varieties, equivariant quantum \(\mathcal D\)-modules, and localization of quantum groups
• Localization for quantum groups at a root of unity
• Espaces Homogènes De Stein Des Groupes De Lie Complexes
• Singular Localization and Intertwining Functors for Reductive Lie Algebras in Prime Characteristic
• Wall-Crossing functors and D-modules
• Koszul Duality Patterns in Representation Theory
• Lie Group Representations on Polynomial Rings
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