Generalised discriminants, deformed quantum CalogeroMoser system and Jack polynomials
Abstract
It is shown that the deformed CalogeroMoserSutherland (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 superJack polynomials are introduced and combinatorial formulas for them and for superJack polynomials are given.
 Publication:

arXiv eprints
 Pub Date:
 July 2003
 arXiv:
 arXiv:mathph/0307036
 Bibcode:
 2003math.ph...7036S
 Keywords:

 Mathematical Physics;
 Mathematics  Mathematical Physics;
 Mathematics  Quantum Algebra;
 81R12
 EPrint:
 30 pages, 1 figure, revised and extended version