Cuspidal representations of rational Cherednik algebras at t=0

TL;DR

This paper investigates finite-dimensional quotients of the rational Cherednik algebra at t=0 supported at a point in the center, revealing their Morita equivalence to cuspidal quotients linked to parabolic subgroups.

Contribution

It establishes a Morita equivalence between certain finite-dimensional quotients of the rational Cherednik algebra at t=0 and cuspidal quotients associated with parabolic subgroups.

Findings

Finite-dimensional quotients at t=0 are supported at a point in the center.

Each such quotient is Morita equivalent to a cuspidal quotient of a related Cherednik algebra.

The work connects algebraic quotients to geometric structures via Morita equivalence.

Abstract

We study those finite dimensional quotients of the rational Cherednik algebra at t=0 that are supported at a point of the centre. It is shown that each such quotient is Morita equivalent to a certain cuspidal quotient of a rational Cherednik algebra associated to a parabolic subgroup of W.