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Generalised discriminants, deformed Calogero-Moser-Sutherland operators and super-Jack polynomials. (English) Zbl 1069.05076
Summary: It is shown that the deformed Calogero-Moser-Sutherland (CMS) operators can be described as the restrictions on certain affine subvarieties (called generalised discriminants) of the usual CMS operators for infinite number of particles. The ideals of these varieties are shown to be generated by the Jack symmetric functions related to the Young diagrams with special geometry. A general structure of the ideals which are invariant under the action of the quantum CMS integrals is discussed in this context. The shifted super-Jack polynomials are introduced and combinatorial formulas for them and for super-Jack polynomials are given.

05E05 Symmetric functions and generalizations
81R12 Groups and algebras in quantum theory and relations with integrable systems
33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.)
Full Text: DOI
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