2013/05/21 by Ivan Losev, Losev, Ivan · 3 citations
Mathematics · #16G99 #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1305.4894
openalex publication_date 2013/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.