# Source Identities and Kernel Functions for the Deformed Koornwinder–van Diejen Models

@article{Atai2019SourceIA, title={Source Identities and Kernel Functions for the Deformed Koornwinder–van Diejen Models}, author={Farrokh Atai}, journal={Communications in Mathematical Physics}, year={2019}, volume={377}, pages={2191-2216} }

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…

## 3 Citations

Eigenfunctions of the van Diejen model generated by gauge and integral transformations

- Mathematics
- 2022

We present how explicit eigenfunctions of the principal Hamiltonian for the BCm relativistic Calogero-Moser-Sutherland model, due to van Diejen, can be constructed using gauge and integral…

Eigenfunctions of a discrete elliptic integrable particle model with hyperoctahedral symmetry

- Mathematics
- 2021

We construct the orthogonal eigenbasis for a discrete elliptic Ruijsenaars type quantum particle Hamiltonian with hyperoctahedral symmetry. In the trigonometric limit the eigenfunctions in question…

Eigenfunctions of a Discrete Elliptic Integrable Particle Model with Hyperoctahedral Symmetry

- MathematicsCommunications in Mathematical Physics
- 2022

We construct the orthogonal eigenbasis for a discrete elliptic Ruijsenaars type quantum particle Hamiltonian with hyperoctahedral symmetry. In the trigonometric limit the eigenfunctions in question…

## References

SHOWING 1-10 OF 28 REFERENCES

Source Identities and Kernel Functions for Deformed (Quantum) Ruijsenaars Models

- Mathematics
- 2013

We consider the relativistic generalization of the quantum AN-1 Calogero–Sutherland models due to Ruijsenaars, comprising the rational, hyperbolic, trigonometric and elliptic cases. For each of these…

Source Identity and Kernel Functions for Elliptic Calogero–Sutherland Type Systems

- Mathematics
- 2010

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…

Source identity and kernel functions for Inozemtsev-type systems

- Mathematics
- 2012

The Inozemtsev Hamiltonian is an elliptic generalization of the differential operator defining the BCN trigonometric quantum Calogero-Sutherland model, and its eigenvalue equation is a natural…

Complete integrability of relativistic Calogero-Moser systems and elliptic function identities

- Mathematics
- 1987

Poincaré-invariant generalizations of the Galilei-invariant Calogero-MoserN-particle systems are studied. A quantization of the classical integralsS1, ...,SN is presented such that the operatorsŜ1,…

Kernel identities for van Diejen’s q-difference operators and transformation formulas for multiple basic hypergeometric series

- Mathematics
- 2011

The kernel function of Cauchy type for type BC is defined as a solution of linear q-difference equations. In this paper, we show that this kernel function intertwines the commuting family of van…

Generalised discriminants, deformed Calogero–Moser–Sutherland operators and super-Jack polynomials

- Mathematics
- 2005

Hilbert-Schmidt Operators vs. Integrable Systems of Elliptic Calogero-Moser Type I. The Eigenfunction Identities

- Mathematics
- 2009

In this series of papers we study Hilbert-Schmidt integral operators acting on the Hilbert spaces associated with elliptic Calogero-Moser type Hamiltonians. As shown in this first part, the integral…

Kernel Functions for Difference Operators of Ruijsenaars Type and Their Applications

- Mathematics
- 2009

A unified approach is given to kernel functions which intertwine Ruijsenaars difference operators of type A and of type BC. As an application of the trigonometric cases, new explicit formulas for…