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)

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Publisher's URL: http://dx.doi.org/10.1093/imrn/rnr140


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
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
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

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