Supports of irreducible spherical representations of rational Cherednik algebras of finite Coxeter groups
Author(s)
Etingof, Pavel I.
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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.
Date issued
2011-11Department
Massachusetts Institute of Technology. Department of MathematicsJournal
Advances in Mathematics
Publisher
Elsevier
Citation
Etingof, Pavel. “Supports of Irreducible Spherical Representations of Rational Cherednik Algebras of Finite Coxeter Groups.” Advances in Mathematics 229, no. 3 (February 2012): 2042–2054.
Version: Author's final manuscript
ISSN
00018708
1090-2082