A unified construction of generalised classical polynomials associated with operators of Calogero-Sutherland type

Abstract

In this paper we consider a large class of many-variable polynomials which contains generalisations of the classical Hermite, Laguerre, Jacobi and Bessel polynomials as special cases, and which occur as the polynomial part in the eigenfunctions of Calogero-Sutherland type operators and their deformations recently found and studied by Chalykh, Feigin, Sergeev, and Veselov. We present a unified and explicit construction of all these polynomials.

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Cited by in corpus (14)

• Kernel functions and Bäcklund transformations for relativistic Calogero-Moser and Toda systems
• Explicit solution of the (quantum) elliptic Calogero-Sutherland model
• Hermite and Laguerre Symmetric Functions Associated with Operators of Calogero-Moser-Sutherland Type
• Source identity and kernel functions for elliptic Calogero-Sutherland type systems
• Deformed Calogero-Sutherland model and fractional Quantum Hall effect
• Orthogonality of super-Jack polynomials and a Hilbert space interpretation of deformed Calogero-Moser-Sutherland operators
• Source identity and kernel functions for Inozemtsev-type systems
• Source identities and kernel functions for deformed (quantum) Ruijsenaars models
• Spectrum and eigenfunctions of the lattice hyperbolic Ruijsenaars-Schneider system with exponential Morse term
• Series Solutions of the Non-Stationary Heun Equation
• Branching Rules for Symmetric Hypergeometric Polynomials
• Generalized Calogero-Moser systems from rational Cherednik algebras
• Source identities and kernel functions for the deformed Koornwinder-van Diejen models
• Wave functions for quantum integrable particle systems via partial confluences of multivariate hypergeometric functions