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Generalised discriminants, deformed quantum Calogero-Moser system and Jack polynomials
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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.
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Exact solutions by integrals of the non-stationary elliptic Calogero-Sutherland equation
Integral representations are constructed for solutions of the non-stationary elliptic Calogero-Sutherland equation, yielding elliptic analogues of Jack polynomials for non-integer coupling values.
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