Bispectrality for deformed Calogero-Moser-Sutherland systems

TL;DR

This paper establishes bispectral duality for certain deformed Calogero-Moser-Sutherland systems, explicitly constructing dual difference operators and Baker-Akhiezer functions for these integrable models.

Contribution

It extends bispectral duality to generalized Calogero-Moser-Sutherland systems with new explicit constructions of dual operators and functions.

Findings

Proves bispectral duality for specific deformed systems

Constructs dual difference operators of Macdonald type

Explicitly constructs Baker-Akhiezer functions for these systems

Abstract

We prove bispectral duality for the generalized Calogero-Moser-Sutherland systems related to configurations $A_{n,2}(m), C_n(l,m)$. The trigonometric axiomatics of Baker-Akhiezer function is modified, the dual difference operators of rational Macdonald type and the Baker-Akhiezer functions related to both series are explicitly constructed.