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Quasi-invariants and quantum integrals of the deformed Calogero--Moser systems

M. Feigin·A. P. Veselov
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Abstract

The rings of quantum integrals of the generalized Calogero-Moser systems related to the deformed root systems ${\cal A}_n(m)$ and ${\cal C}_n(m,l)$ with integer multiplicities and corresponding algebras of quasi-invariants are investigated. In particular, it is shown that these algebras are finitely generated and free as the modules over certain polynomial subalgebras (Cohen-Macaulay property). The proof follows the scheme proposed by Etingof and Ginzburg in the Coxeter case. For two-dimensional systems the corresponding Poincare series and the deformed $m$-harmonic polynomials are explicitly computed.

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M. Feigin, A. P. Veselov. 2003-03-10. Quasi-invariants and quantum integrals of the deformed Calogero--Moser systems. https://arxiv.org/abs/math-ph/0303026

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