Rational Cherednik algebras and Schubert cells

Bellamy, G. (2018) Rational Cherednik algebras and Schubert cells. Algebras and Representation Theory, (doi:10.1007/s10468-018-9831-3) (Early Online Publication)

[img]
Preview
Text
169391.pdf - Published Version
Available under License Creative Commons Attribution.

857kB

Abstract

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.
Status:Early Online Publication
Refereed:Yes
Glasgow Author(s) Enlighten ID:Bellamy, Dr Gwyn
Authors: Bellamy, G.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Algebras and Representation Theory
Publisher:Springer
ISSN:1386-923X
ISSN (Online):1572-9079
Published Online:30 October 2018
Copyright Holders:Copyright © 2018 The Authors
First Published:First published in Algebras and Representation Theory 2019
Publisher Policy:Reproduced under a Creative Commons License

University Staff: Request a correction | Enlighten Editors: Update this record