Singular polynomials from orbit spaces
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.
Cite
@article{arxiv.1110.1946,
title = {Singular polynomials from orbit spaces},
author = {M. Feigin and A. Silantyev},
journal= {arXiv preprint arXiv:1110.1946},
year = {2012}
}
Comments
17 pages; a relevant reference is added and other minor changes; to appear in Compositio Math