Quasiharmonic polynomials for Coxeter groups and representations of Cherednik algebras

Details Quasiharmonic polynomials for Coxeter groups and representations of Cherednik algebras Quasiharmonic polynomials for Coxeter groups and representations of Cherednik algebras

2005-05-10

arxiv.org/abs/math/0505173v4

Mathematics

Representation Theory

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

Scientific paper

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.

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