Endomorphisms of Verma modules for rational Cherednik algebras

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.

This paper constitutes what used to be those sections on the endomorphisms of Verma modules in the paper "Rational Cherednik algebras and Schubert cells" arXiv:1210.3870, in order to make the latter paper more concise. The main result has been strengthen somewhat