Categorifications and cyclotomic rational double affine Hecke algebras.
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Publication:295797
DOI10.1007/s00222-015-0623-7zbMath1347.20004arXiv1305.4456OpenAlexW1745690065MaRDI QIDQ295797
Michela Varagnolo, Eric Vasserot, Peng Shan, Raphaël Rouquier
Publication date: 13 June 2016
Published in: Inventiones Mathematicae (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1305.4456
Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Hecke algebras and their representations (20C08) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67)
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Cites Work
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- Highest weight \(\mathfrak{sl }_2\)-categorifications. I: Crystals
- The degenerate analogue of Ariki's categorification theorem
- Generalized Jack polynomials and the representation theory of rational Cherednik algebras
- Morita equivalences of Ariki-Koike algebras.
- A conjecture for \(q\)-decomposition matrices of cyclotomic \(v\)-Schur algebras.
- The combinatorics of category \({\mathcal O}\) over symmetrizable Kac-Moody algebras
- Integral and graded quasi-hereditary algebras. I
- Categories of modules over an affine Kac-Moody algebra and finiteness of the Kazhdan-Lusztig tensor product
- Quantization of Lie bialgebras. VI: Quantization of generalized Kac-Moody algebras
- Schur-Weyl duality for higher levels
- Blocks of cyclotomic Hecke algebras and Khovanov-Lauda algebras.
- Structure of representations with highest weight of infinite-dimensional Lie algebras
- Symmetric cyclotomic Hecke algebras
- Cyclotomic \(q\)-Schur algebras
- Centers and translation functors for the category \({\mathcal O}\) over Kac-Moody algebras
- Module categories, weak Hopf algebras and modular invariants
- On primitive ideals.
- On the category \(\mathcal O\) for rational Cherednik algebras.
- Kazhdan-Lusztig conjecture for symmetrizable Kac-Moody Lie algebras. III: Positive rational case.
- On category \(\mathcal O\) for cyclotomic rational Cherednik algebras.
- Koszul duality of affine Kac-Moody algebras and cyclotomic rational double affine Hecke algebras
- Parabolic induction and restriction functors for rational Cherednik algebras.
- Derived equivalences for symmetric groups and \(\mathfrak{sl}_2\)-categorification.
- Blocks of cyclotomic Hecke algebras.
- Cyclotomic double affine Hecke algebras and affine parabolic category \(\mathcal O\).
- Quiver Hecke Algebras and 2-Lie Algebras
- Tensor Structures Arising from Affine Lie Algebras. I
- Highest weight 𝔰𝔩₂-categorifications II: Structure theory
- A diagrammatic approach to categorification of quantum groups I
- Centers of degenerate cyclotomic Hecke algebras and parabolic category 𝒪
- Character formulas for tilting modules over Kac-Moody algebras
- Lusztig conjectures, old and new, I.
- Tilting modules for cyclotomic Schur algebras
- ROUQUIER’S CONJECTURE AND DIAGRAMMATIC ALGEBRA
- Symplectic reflection algebras and affine Lie algebras
- Heisenberg algebras and rational double affine Hecke algebras
- Crystals of Fock spaces and cyclotomic rational double affine Hecke algebras
- Cyclotomic Nazarov-Wenzl Algebras
- Des catégories abéliennes
