Proof of Varagnolo-Vasserot conjecture on cyclotomic categories O
arXiv:1305.4894
Abstract
We prove an asymptotic version of a conjecture by Varagnolo and Vasserot on an equivalence between the category O for a cyclotomic Rational Cherednik algebra and a suitable truncation of an affine parabolic category O. We prove an asymptotic version of a conjecture by Varagnolo and Vasserot on an equivalence between the category O for a cyclotomic Rational Cherednik algebra and a suitable truncation of an affine parabolic category O that, in particular, implies Rouquier's conjecture on the decomposition numbers in the former. Our proof uses two ingredients: an extension of Rouquier's deformation approach as well as categorical actions on highest weight categories and related combinatorics. This text replaces arXiv:1207.1299.
50 pages. arXiv admin note: substantial text overlap with arXiv:1207.1299, v2 minor changes, v2 has a serious gap in 10.4, see Remark 1.2 in v3. v3 has a simpler proof, 33 pages, v4 accepted version, some changes
References in corpus (4)
Cited by in corpus (12)
- Rouquier's conjecture and diagrammatic algebra
- Etingof conjecture for quantized quiver varieties
- Modular representation theory in type A via Soergel bimodules
- Supports of simple modules in cyclotomic Cherednik categories O
- The many graded cellular bases of Hecke algebras
- Representation theory of the cyclotomic Cherednik algebra via the Dunkl-Opdam subalgebra
- Geometric representations of graded and rational Cherednik algebras
- Harish-Chandra bimodules over rational Cherednik algebras
- Character formulas and Bernstein-Gelfand-Gelfand resolutions for Cherednik algebra modules
- On modular categories O for quantized symplectic resolutions
- Abelian localization for cyclotomic Cherednik algebras
- New realization of cyclotomic -Schur algebras I