Quasiharmonic polynomials for Coxeter groups and representations of Cherednik algebras

Arkady Berenstein; Yurii Burman

Quasiharmonic polynomials for Coxeter groups and representations of Cherednik algebras

Representation Theory 2007-08-15 v4 Quantum Algebra

Authors: Arkady Berenstein , Yurii Burman

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.

Keywords

cherednik algebras coxeter groups quasiharmonic polynomials harmonic polynomials elementary symmetric polynomials representations

Cite

@article{arxiv.math/0505173,
  title  = {Quasiharmonic polynomials for Coxeter groups and representations of Cherednik algebras},
  author = {Arkady Berenstein and Yurii Burman},
  journal= {arXiv preprint arXiv:math/0505173},
  year   = {2007}
}

Comments

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

Quasiharmonic polynomials for Coxeter groups and representations of Cherednik algebras

Abstract

Keywords

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