# Source identities and kernel functions for the deformed Koornwinder-van Diejen models

## TL;DR

This paper develops explicit eigenfunctions and kernel identities for generalized BC-type relativistic Calogero-Moser-Sutherland models, extending known results to elliptic and deformed cases.

## Contribution

It introduces new eigenfunctions and kernel identities for generalized Koornwinder-van Diejen models, including deformations and elliptic cases.

## Key findings

- Explicit eigenfunctions constructed for generalized models
- Kernel function identities established for special cases
- Deformation of operators and kernel functions generalized

## Abstract

We consider generalizations of the $BC$-type relativistic Calogero-Moser-Sutherland models, comprising of the rational, trigonometric, hyperbolic, and elliptic cases, due to Koornwinder and van Diejen, and construct an explicit eigenfunction for these generalizations. In special cases, we find the various kernel function identities, and also a Chalykh-Feigin-Sergeev-Veselov type deformation of these operators and their corresponding kernel functions, which generalize the known kernel functions for the Koornwinder-van Diejen models.