Endomorphisms of Verma modules for rational Cherednik algebras
In this paper, the author studies endomorphisms of Verma modules for rational Cherednik algebras of complex reflection groups, for the special value \(t=0\) of the defining parameter. For this value of the parameter, the rational Cherednik algebra is a finite module over the center of the algebra. The main result of the paper shows that, in many cases, the center of the rational Cherednik algebra surjects onto the endomorphism algebra of a Verma module. In some special cases, it is shown that the endomorphism algebra of a Verma module is a polynomial ring and the Verma module is free over this polynomial ring, of rank equal to the cardinality of the complex reflection group used to define the rational Cherednik algebra. The results of the paper are motivated by their description in the context of derived intersections of Lagrangian subvarieties of the generalized Calogero-Moser spaces.
scientific article; zbMATH DE number 6339819
scientific article