We study equivalences for category of the rational Cherednik algebras of type : a highest weight equivalence between and for and an action of on an explicit non-empty Zariski open set of parameters ; a derived equivalence between and whenever and have integral difference; a highest weight equivalence between and a parabolic category for the general linear group, under a non-rationality assumption on the parameter . As a consequence, we confirm special cases of conjectures of Etingof and of Rouquier.
Cite this article
Iain G. Gordon, Ivan Losev, On category for cyclotomic rational Cherednik algebras. J. Eur. Math. Soc. 16 (2014), no. 5, pp. 1017–1079DOI 10.4171/JEMS/454