Доклад Ивана Лосева "Cherednik vs Hecke"

Abstract: I am going to explore connections between two classes of algebras associated to complex reflection groups: Hecke algebras introduced in this generality by Broue, Malle and Rouquier, and Rational Cherednik algebras introduced by Etingof and Ginzburg. These algebras are related via the so called KZ functor between suitable categories of modules. In the first half of my talk I will introduce the algebras and the functor. In the second half I will explain various properties of the KZ functor. The talk is based on three arXiv preprints: 1409.3965, 1407.6375, 1406.7502. It is going to be reasonably self-contained and in Russian.