On category O for cyclotomic rational Cherednik algebras
arXiv:1109.2315
Abstract
We study equivalences for category O_p of the rational Cherednik algebras H_p of type G_l(n) = μ_l^n\rtimes S_n: a highest weight equivalence between O_p and O_{σ(p)} for σ\in S_l and an action of S_l on a non-empty Zariski open set of parameters p; a derived equivalence between O_p and O_{p'} whenever p and p' have integral difference; a highest weight equivalence between O_p and a parabolic category O for the general linear group, under a non-rationality assumption on the parameter p. As a consequence, we confirm special cases of conjectures of Etingof and of Rouquier.
61 pages; v2 64 pages, new material added; to appear J. Eur. Math. Soc
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Cited by in corpus (20)
- Quiver Schur algebras and q-Fock space
- Etingof conjecture for quantized quiver varieties
- On categories O for quantized symplectic resolutions
- Supports of simple modules in cyclotomic Cherednik categories O
- Proof of Varagnolo-Vasserot conjecture on cyclotomic categories O
- Representation theory of the cyclotomic Cherednik algebra via the Dunkl-Opdam subalgebra
- Etingof conjecture for quantized quiver varieties II: affine quivers
- Highest weight sl_2-categorifications I: crystals
- A combinatorial decomposition of higher level Fock spaces
- Short Star-Products for Filtered Quantizations, I
- Quantizations of regular functions on nilpotent orbits
- Dimensions of irreducible modules over W-algebras and Goldie ranks
- Harish-Chandra bimodules over rational Cherednik algebras
- Towards multiplicities for categories O of cyclotomic rational Cherednik algebras
- On modular categories O for quantized symplectic resolutions
- Derived equivalence for quantum symplectic resolutions
- Real variations of stability conditions for noncommutative symplectic resolutions
- Abelian localization for cyclotomic Cherednik algebras
- Cyclotomic Carter-Payne homomorphisms
- Equivariant deformation quantization and coadjoint orbit method