TL;DR
This paper reviews the representation theory of restricted rational Cherednik algebras, highlighting their geometric connections, open problems, and explicit results in specific cases, advancing understanding of their algebraic and geometric properties.
Contribution
It provides a comprehensive overview of the theory, discusses open problems, and presents explicit results for cyclic and dihedral cases, contributing to the field's development.
Findings
Connection to Calogero-Moser space geometry
Explicit results for cyclic and dihedral cases
Open problems and conjectures outlined
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.
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