Quasiharmonic polynomials for Coxeter groups and representations of Cherednik algebras

Berenstein, Arkady; Burman, Yurii

doi:10.1090/S0002-9947-09-04620-0

Quasiharmonic polynomials for Coxeter groups and representations of Cherednik algebras
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by Arkady Berenstein and Yurii Burman PDF

Trans. Amer. Math. Soc. 362 (2010), 229-260 Request permission

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 each Coxeter group — 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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