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)

Abstract

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
• Status: Published
• Refereed: Yes
• 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
• ISSN: 0010-437X
• 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

Related URLs

• http://arxiv.org/abs/1110.1946