Common Algebraic Structure for the Calogero-Sutherland Models

Abstract

We investigate common algebraic structure for the rational and trigonometric Calogero-Sutherland models by using the exchange-operator formalism. We show that the set of the Jack polynomials whose arguments are Dunkl-type operators provides an orthogonal basis for the rational case.

7 pages, LaTeX, no figures, some text and references added, minor misprints corrected

References in corpus (2)

• Exact operator solution of the Calogero-Sutherland model
• Rodrigues Formula for Hi-Jack Symmetric Polynomials Associated with the Quantum Calogero Model

Cited by in corpus (32)

• Quantum Calogero-Moser Models: Integrability for all Root Systems
• Exact Solutions of the 2D Dunkl--Klein--Gordon Equation: The Coulomb Potential and the Klein--Gordon Oscillator
• Exact Solution of the Relativistic Dunkl Oscillator in $(2+1)$ Dimensions
• Dunkl-Klein-Gordon equation in three-dimensions: The Klein-Gordon oscillator and Coulomb Potential
• Thermal Properties of Relativistic Dunkl Oscillators
• $SU(1,1)$ solution for the Dunkl-Coulomb problem in two dimensions and its coherent states
• Quantum Quench of the trap frequency in the harmonic Calogero model
• Dunkl-Graphene in constant magnetic field
• Exact solutions of the Schrödinger Equation with Dunkl Derivative for the Free-Particle Spherical Waves, the Pseudo-Harmonic Oscillator and the Mie-type Potential
• Landau levels for the $(2+1)$ Dunkl-Klein-Gordon oscillator
• Ideal Bose Gas and Blackbody Radiation in the Dunkl Formalism
• The condensation of ideal Bose gas in a gravitational field in the framework of Dunkl-statistic
• Dunkl-Pauli Equation in the Presence of a Magnetic Field
• Effect of the two-parameter generalized Dunkl derivative on the two-dimensional Schrödinger equation
• A unified construction of generalised classical polynomials associated with operators of Calogero-Sutherland type
• Dunkl-Schrödinger equation with time-dependent harmonic oscillator potential
• Time-Dependent Dunkl-Schrödinger Equation with an Angular-Dependent Potential
• Dunkl-Schrodinger Equation in Higher Dimension
• The Condensation of Ideal Dunkl-Bose Gas in Power-Law Traps
• On Dunkl-Bose-Einstein Condensation in Harmonic Traps
• New Non-Symmetric Orthogonal Basis for the Calogero Model with Distinguishable Particles
• One-dimensional Dunkl Quantum Mechanics: A Path Integral Approach
• The Yangian Symmetry in the Spin Calogero Model and its Applications
• Explicit formulas for the eigenfunctions of the N-body Calogero model
• Intertwining Operators for a Degenerate Double Affine Hecke Algebra and Multivariable Orthogonal Polynomials
• Dunkl-Klein-Gordon Equation in Higher Dimensions
• Time-dependent Dunkl-Pauli Oscillator
• Bounding the Wigner Deformation Parameter in Harmonically Trapped Bose Gases
• Braid Structure and Raising-Lowering Operator Formalism in Sutherland Model
• Faceting Transition in an Exactly Solvable Terrace-Ledge-Kink model
• Spectral and Thermal Analysis of the Morse Potential within the Dunkl Formalism: Analytical Approximations and Applications
• Superdiffusion and antidiffusion in an aligned active suspension