Orthogonality of the Hi-Jack Polynomials Associated with the Calogero Model

DOI10.1143/JPSJ.66.345zbMath0957.33010arXivcond-mat/9706133MaRDI QIDQ4491512

Hideaki Ujino, Miki Wadati

Publication date: 26 July 2000

Published in: Journal of the Physical Society of Japan (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/cond-mat/9706133

zbMATH Keywords

generalized Hermite polynomialsCalogero modelJack polynomialsdominance orderDunkl operatorstriangularityorthogonal symmetric polynomialssimultaneous eigenfunctionHi-Jack polynomials

Mathematics Subject Classification ID

Connections of hypergeometric functions with groups and algebras, and related topics (33C80)

Related Items (11)

AN ALGEBRAIC APPROACH TO THE EIGENSTATES OF THE CALOGERO MODEL ⋮ Partition functions of Polychronakos like spin chains associated with polarized spin reversal operators ⋮ The spin Sutherland model of \(D_N\) type and its associated spin chain ⋮ Generalized Hermite polynomials in superspace as eigenfunctions of the supersymmetric rational CMS model ⋮ New nonsymmetric orthogonal basis for the Calogero model with distinguishable particles ⋮ Exactly solvable \(D_N\)-type quantum spin models with long-range interaction ⋮ Intertwining operators for a degenerate double affine Hecke algebra and multivariable orthogonal polynomials ⋮ An algebraic approach to the non-symmetric Macdonald polynomial ⋮ Rodrigues formulas for the non-symmetric multivariable polynomials associated with the \(\text{BC}_N\)-type root system ⋮ Symmetric Fock space and orthogonal symmetric polynomials associated with the Calogero model ⋮ Exact solution of D N-type quantum Calogero model through a mapping to free harmonic oscillators

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