Source identity and kernel functions for elliptic Calogero-Sutherland type systems

Abstract

Kernel functions related to quantum many-body systems of Calogero-Sutherland type are discussed, in particular for the elliptic case. The main result is an elliptic generalization of an identity due to Sen that is a source for many such kernel functions. Applications are given, including simple exact eigenfunctions and corresponding eigenvalues of Chalykh-Feigin-Veselov-Sergeev-type deformations of the elliptic Calogero-Sutherland model for special parameter values.

v1: 12 pages. v2: 13 pages; typos corrected; one reference added

References in corpus (6)

• Deformed quantum Calogero-Moser problems and Lie superalgebras
• Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications
• Q-operator and factorised separation chain for Jack polynomials
• A unified construction of generalised classical polynomials associated with operators of Calogero-Sutherland type
• Remarkable identities related to the (quantum) elliptic Calogero-Sutherland model
• Quantum integrability of the deformed elliptic Calogero-Moser problem

Cited by in corpus (10)

• Explicit solution of the (quantum) elliptic Calogero-Sutherland model
• Deformed Calogero-Sutherland model and fractional Quantum Hall effect
• Super-Macdonald polynomials: Orthogonality and Hilbert space interpretation
• Source identity and kernel functions for Inozemtsev-type systems
• A new perspective on the integrability of Inozemtsev's elliptic spin chain
• Source identities and kernel functions for deformed (quantum) Ruijsenaars models
• Series Solutions of the Non-Stationary Heun Equation
• Source identities and kernel functions for the deformed Koornwinder-van Diejen models
• Exact solutions by integrals of the non-stationary elliptic Calogero-Sutherland equation
• Conformal field theory, solitons, and elliptic Calogero--Sutherland models