Supports of irreducible spherical representations of rational Cherednik algebras of finite Coxeter groups

[摘要] In this paper we determine the support of the irreducible spherical representation (i.e., the irreducible quotient of the polynomial representation) of the rational Cherednik algebra of a finite Coxeter group for any value of the parameter c. In particular, we determine for which values of c this representation is finite dimensional. This generalizes a result of Varagnolo and Vasserot (2009) [20], who classified finite dimensional spherical representations in the case of Weyl groups and equal parameters (i.e., when c is a constant function). Our proof is based on the Macdonald–Mehta integral and the elementary theory of distributions.

[发布机构] Elsevier