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arXiv · 1305.4894

Proof of Varagnolo-Vasserot conjecture on cyclotomic categories O

Ivan Losev
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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.

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Ivan Losev. 2013-05-21. Proof of Varagnolo-Vasserot conjecture on cyclotomic categories O. https://arxiv.org/abs/1305.4894

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