  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.
