Source identities and kernel functions for deformed (quantum) Ruijsenaars models

Abstract

We consider the relativistic generalization of the quantum $A_{N-1}$ Calogero-Sutherland models due to Ruijsenaars, comprising the rational, hyperbolic, trigonometric and elliptic cases. For each of these cases, we find an exact common eigenfunction for a generalization of Ruijsenaars analytic difference operators that gives, as special cases, many different kernel functions; in particular, we find kernel functions for Chalykh- Feigin-Veselov-Sergeev-type deformations of such difference operators which generalize known kernel functions for the Ruijsenaars models. We also discuss possible applications of our results.

24 pages

References in corpus (3)

• Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications
• On the N=2 superconformal index and eigenfunctions of the elliptic RS model
• Singular Eigenfunctions of Calogero-Sutherland Type Systems and How to Transform Them into Regular Ones

Cited by in corpus (5)

• Super-Macdonald polynomials: Orthogonality and Hilbert space interpretation
• Higher order deformed elliptic Ruijsenaars operators
• Source identities and kernel functions for the deformed Koornwinder-van Diejen models
• On R-matrix identities related to elliptic anisotropic spin Ruijsenaars-Macdonald operators
• From Kajihara's transformation formula to deformed Macdonald-Ruijsenaars and Noumi-Sano operators