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

TL;DR

This paper develops elliptic kernel functions for Calogero-Sutherland systems, generalizing known identities, and provides exact eigenfunctions and eigenvalues for certain deformations of these quantum many-body models.

Contribution

It introduces an elliptic generalization of Sen's identity, enabling new kernel functions and exact solutions for specific elliptic Calogero-Sutherland models.

Findings

Derived elliptic kernel functions for Calogero-Sutherland systems

Obtained exact eigenfunctions and eigenvalues for deformed models

Extended known identities to the elliptic case

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.