Quasiharmonic polynomials for Coxeter groups and representations of Cherednik algebras

Abstract

We introduce and study deformations of finite-dimensional modules over rational Cherednik algebras. Our main tool is a generalization of usual harmonic polynomials for Coxeter groups -- the so-called quasiharmonic polynomials. A surprising application of this approach is the construction of canonical elementary symmetric polynomials and their deformations for all Coxeter groups.

A key conjecture is proved, based on Pavel Etingof's idea (now it is Theorem 1.13). The Section 2 -- dihedral group case -- is simplified