Proof of Varagnolo–Vasserot conjecture on cyclotomic categories O

Ivan Losev ^[1]
1. [1] Northeastern University
Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 22, Nº. 2, 2016, págs. 631-668
Idioma: inglés
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Resumen
- We prove an asymptotic version of a conjecture by Varagnolo and Vasserot on an equivalence between the category OO for a cyclotomic rational Cherednik algebra and a suitable truncation of an affine parabolic category OO 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.