Quasiharmonic polynomials for Coxeter groups and representations of Cherednik algebras

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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

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Representation Theory, Quantum Algebra

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http://salesiana.dossiersoluciones.com/handle/123456789/136013

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0505173
 http://arxiv.org/abs/math/0505173

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arXiv