The Calogero Model: Integrable Structures and Orthogonal Basis

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Integrability, algebraic structures and orthogonal basis of the Calogero model are studied by the quantum Lax and Dunkl operator formulations. The commutator algebra among operators including conserved operators and creation-annihilation operators has the structure of the W-algebra. Through an algebraic construction of the simultaneous eigenfunctions of all the commuting conserved operators, we show that the Hi-Jack (hidden-Jack) polynomials, which are an multi-variable generalization of the Hermite polynomials, form the orthogonal basis.
14pages, LaTeX file using fleqn.sty, to appear in the proceedings of the Workshop on the Calogero-Moser-Sutherland models in the CRM Series in Mathematical Physics (Springer-Verlag)

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Statistical Mechanics, High Energy Physics - Theory, Quantum Algebra, Exactly Solvable and Integrable Systems

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http://salesiana.dossiersoluciones.com/handle/123456789/151826

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/cond-mat/9706156
 http://arxiv.org/abs/cond-mat/9706156

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arXiv