On unitary submodules in the polynomial representations of rational cherednik algebras

Feigin, M. and Shramov, C. (2012) On unitary submodules in the polynomial representations of rational cherednik algebras. International Mathematics Research Notices, 15, pp. 3375-3414. (doi: 10.1093/imrn/rnr140)

Abstract

We consider representations of rational Cherednik algebras that are particular ideals in the ring of polynomials. We investigate convergence of the integrals that express the Gaussian inner product on these representations. We derive that the integrals converge for the minimal submodules in types B and D for the singular values suggested by Cherednik with at most one exception; hence the corresponding modules are unitary. The analogous result on unitarity of the minimal submodules in type A was obtained by Etingof and Stoica; we give a different proof of convergence of the Gaussian product in this case. We also obtain partial results on unitarity of the minimal submodule in the case of exceptional Coxeter groups and group B with unequal parameters.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Feigin, Professor Misha
• Authors: Feigin, M., and Shramov, C.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: International Mathematics Research Notices
• Publisher: Oxford University Press
• ISSN: 1073-7928
• Published Online: 01 August 2011
• Copyright Holders: Copyright © 2012 Oxford University Press
• First Published: First published in International Mathematics Research Notices
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher