Geodesic
On category $\mathcal{O}$ for cyclotomic rational Cherednik algebras
Journal of the European Mathematical Society, Tome 16 (2014) no. 5, pp. 1017-1079

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We study equivalences for category Op​ of the rational Cherednik algebras Hp​ of type Gl​(n)=(μl​)n⋊Sn​: a highest weight equivalence between Op​ and Oσ(p)​ for σ∈Sl​ and an action of Sl​ on an explicit non-empty Zariski open set of parameters p; a derived equivalence between Op​ and Op′​ whenever p and p′ have integral difference; a highest weight equivalence between Op​ and a parabolic category O for the general linear group, under a non-rationality assumption on the parameter p. As a consequence, we confirm special cases of conjectures of Etingof and of Rouquier.
DOI : 10.4171/jems/454
Classification : 16-XX, 00-XX, 17-XX
Keywords: Cherednik algebra, category O, derived category, deformation quantization, categorification 
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     author = {Iain G. Gordon and Ivan Losev},
     title = {On category $\mathcal{O}$ for cyclotomic rational {Cherednik} algebras},
     journal = {Journal of the European Mathematical Society},
     pages = {1017--1079},
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Iain G. Gordon; Ivan Losev. On category $\mathcal{O}$ for cyclotomic rational Cherednik algebras. Journal of the European Mathematical Society, Tome 16 (2014) no. 5, pp. 1017-1079. doi: 10.4171/jems/454

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