Singular polynomials from orbit spaces

Feigin, M. and Silantyev, A. (2012) Singular polynomials from orbit spaces. Compositio Mathematica, 148(6), pp. 1867-1879. (doi: 10.1112/S0010437X1200036X)

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We consider the polynomial representation S(V*) of the rational Cherednik algebra H_c(W) associated to a finite Coxeter group W at constant parameter c. We show that for any degree d of W and nonnegative integer m the space S(V*) contains a single copy of the reflection representation V of W spanned by the homogeneous singular polynomials of degree d-1+hm, where h is the Coxeter number of W; these polynomials generate an H_c(W) submodule with the parameter c=(d-1)/h+m. We express these singular polynomials through the Saito polynomials that are flat coordinates of the Saito metric on the orbit space V/W. We also show that this exhausts all the singular polynomials in the isotypic component of the reflection representation V for any constant parameter c.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Feigin, Professor Misha
Authors: Feigin, M., and Silantyev, A.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Compositio Mathematica
Publisher:Cambridge University Press
Published Online:01 October 2012
Copyright Holders:Copyright © 2012 Cambridge University Press
First Published:First published in Compositio Mathematica
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher
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