Resumen de Proof of Varagnolo–Vasserot conjecture on cyclotomic categories O

Ivan Losev

• 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.