Cherednik algebras and Yangians

Abstract

We construct a functor from the category of modules over the trigonometric (resp., rational) Cherednik algebra of type gll to the category of integrable modules of level l over a Yangian for the loop algebra sln (resp., over a subalgebra of this loop Yangian) and we establish that it is an equivalence of categories if l+2 < n. Finally, we treat the case of the rational Cherednik algebras of type Al−1.