Generalized Calogero-Moser systems from rational Cherednik algebras

Details Generalized Calogero-Moser systems from rational Cherednik algebras Generalized Calogero-Moser systems from rational Cherednik algebras

2008-09-22

arxiv.org/abs/0809.3487v2

Mathematics

Quantum Algebra

36 pages; the main change is an improvement of section 7 so that it now deals with an arbitrary complex reflection group; Sele

Scientific paper

We consider ideals of polynomials vanishing on the W-orbits of the intersections of mirrors of a finite reflection group W. We determine all such ideals which are invariant under the action of the corresponding rational Cherednik algebra hence form submodules in the polynomial module. We show that a quantum integrable system can be defined for every such ideal for a real reflection group W. This leads to known and new integrable systems of Calogero-Moser type which we explicitly specify. In the case of classical Coxeter groups we also obtain generalized Calogero-Moser systems with added quadratic potential.

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