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arXiv:math/0505173 [math.RT]AbstractReferencesReviewsResources

Quasiharmonic polynomials for Coxeter groups and representations of Cherednik algebras

Arkady Berenstein, Yurii Burman

Published 2005-05-10, updated 2007-08-14Version 4

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.

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
Categories: math.RT, math.QA
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