Rational Cherednik algebras and Schubert cells

Bellamy, G. (2019) Rational Cherednik algebras and Schubert cells. Algebras and Representation Theory, 22(6), pp. 1533-1567. (doi: 10.1007/s10468-018-9831-3)

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The representation theory of rational Cherednik algebras of type A at t = 0 gives rise, by considering supports, to a natural family of smooth Lagrangian subvarieties of the Calogero-Moser space. The goal of this article is to make precise the relationship between these Lagrangian families and Schubert cells in the adelic Grassmannian. In order to do this we show that the isomorphism, as constructed by Etingof and Ginzburg, from the spectrum of the centre of the rational Cherednik algebra to the Calogero-Moser space is compatible with the factorization property of both of these spaces. As a consequence, the space of homomorphisms between certain representations of the rational Cherednik algebra can be identified with functions on the intersection of some Schubert cells.

Item Type:Articles
Additional Information:The author was supported by the EPSRC grant EP-H028153.
Glasgow Author(s) Enlighten ID:Bellamy, Professor Gwyn
Authors: Bellamy, G.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Algebras and Representation Theory
ISSN (Online):1572-9079
Published Online:30 October 2018
Copyright Holders:Copyright © 2018 The Authors
First Published:First published in Algebras and Representation Theory 22(6): 1533-1567
Publisher Policy:Reproduced under a Creative Commons License

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