Ivan Losev
Published 2012-07-05, updated 2013-05-22Version 3
Varagnolo and Vasserot conjectured an equivalence between the category O for a cyclotomic Rational Cherednik algebra and a truncation of an affine parabolic category O of type A. In this paper we reduce their conjecture to some purely combinatorial conjecture. Our principal tool for the reduction is the theory of categorical sl_2-actions on highest weight categories. Then we prove our combinatorial conjecture in some cases.
Comments: This paper has been withdrawn by the author. 25 pages; v2, 36 pages, substantial changes, more material added, replaced by arXiv:1305.4894
Peter-Weyl theorem for Iwahori groups and highest weight categories
Abelian envelopes of exact categories and highest weight categories
Highest weight categories and stability conditions
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