Restricted rational Cherednik algebras

Abstract

We give an overview of the representation theory of restricted rational Cherednik algebras. These are certain finite-dimensional quotients of rational Cherednik algebras at $t=0$. Their representation theory is connected to the geometry of the Calogero–Moser space, and there is a lot of evidence that they contain certain information about Hecke algebras even though the precise connection is so far unclear. We outline the basic theory along with some open problems and conjectures, and give explicit results in the cyclic and dihedral cases.