Rodrigues Formula for Hi-Jack Symmetric Polynomials Associated with the Quantum Calogero Model

Abstract

The Hi-Jack symmetric polynomials, which are associated with the simultaneous eigenstates for the first and second conserved operators of the quantum Calogero model, are studied. Using the algebraic properties of the Dunkl operators for the model, we derive the Rodrigues formula for the Hi-Jack symmetric polynomials. Some properties of the Hi-Jack polynomials and the relationships with the Jack symmetric polynomials and with the basis given by the QISM approach are presented. The Hi-Jack symmetric polynomials are strong candidates for the orthogonal basis of the quantum Calogero model.

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References in corpus (2)

• Exact operator solution of the Calogero-Sutherland model
• Excited States of Calogero-Sutherland Model and Singular Vectors of the $W_N$ Algebra

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• Orthogonal basis for the energy eigenfunctions of the Chern-Simons matrix model
• Orthogonal Symmetric Polynomials Associated with the Calogero Model
• Bosonic realization of algebras in the Calogero model
• Interacting Particles on the Line and Dunkl Intertwining Operator of Type A: Application to the Freezing Regime
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• A Super-Integrable Discretization of the Calogero Model
• Coherent States and Geometric Phases in Calogero-Sutherland Model
• Integrable Quantum Hydrodynamics in Two Dimensional Phase Space
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