Endomorphisms of Verma modules for rational Cherednik algebras

TL;DR

This paper investigates the structure of endomorphism algebras of Verma modules for rational Cherednik algebras at t=0, revealing their relation to the algebra's center and geometric Lagrangian subvarieties.

Contribution

It demonstrates that these endomorphism algebras are often quotients of the Cherednik algebra's center and connects them to Lagrangian subvarieties in Calogero-Moser space.

Findings

Endomorphism algebras are quotients of the Cherednik algebra's center.

These algebras define Lagrangian subvarieties in Calogero-Moser space.

Results are motivated by derived intersection theory of Lagrangians.

Abstract

We study the endomorphism algebra of Verma modules for rational Cherednik algebras at t=0. It is shown that, in many cases, these endomorphism algebras are quotients of the centre of the rational Cherednik algebra. Geometrically, they define Lagrangian subvariaties of the generalized Calogero-Moser space. In the introduction, we motivate our results by describing them in the context of derived intersections of Lagrangians.