Hecke algebras and symplectic reflection algebras

Abstract

The current article is a short survey on the theory of Hecke algebras, and in particular Kazhdan-Lusztig theory, and on the theory of symplectic reflection algebras, and in particular rational Cherednik algebras. The emphasis is on the connections between Hecke algebras and rational Cherednik algebras that could allow us to obtain a generalised Kazhdan-Lusztig theory, or at least its applications, for all complex reflection groups.

This survey was written for the Proceedings of the MSRI Introductory Workshop in Noncommutative Algebraic Geometry and Representation Theory (2013)