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Generalized Calogero–Moser systems from rational Cherednik algebras

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Abstract

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 that 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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  1. School of Mathematics and Statistics, University of Glasgow, 15 University Gardens, Glasgow, G12 8QW, UK

    Misha Feigin

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Feigin, M. Generalized Calogero–Moser systems from rational Cherednik algebras. Sel. Math. New Ser. 18, 253–281 (2012). https://doi.org/10.1007/s00029-011-0074-y

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