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On m-quasiinvariants of Coxeter groups

Pavel Etingof·Victor Ginzburg
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Abstract

Let W be a finite Coxeter group in a Euclidean vector space V, and m a W-invariant Z_+-valued function on the set of reflections in W. Chalyh and Veselov introduced in an interesting algebra Q_m, called the algebra of m-quasiinvariants for W. This is the algebra of quantum integrals of the rational Calogero-Moser system with coupling constants m. In a recent paper math-ph/0105014, Feigin and Veselov proposed a number of interesting conjectures concerning the structure of Q_m, and verified them for dihedral groups and constant functions m. Our goal is to prove some of these conjectures in the general case.

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Pavel Etingof, Victor Ginzburg. 2001-06-20. On m-quasiinvariants of Coxeter groups. https://arxiv.org/abs/math/0106175

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