Elliptic Integrable Systems and Special Functions

TL;DR

This paper introduces elliptic integrable systems, focusing on quantum Calogero-Moser-Sutherland models and their relation to special functions, providing an accessible overview and highlighting open research problems.

Contribution

It offers an accessible introduction to elliptic integrable models and their associated special functions, including recent developments and open questions in the field.

Findings

Connection between elliptic models and special functions clarified

Relativistic generalizations of models discussed

Open problems identified for future research

Abstract

We discuss elliptic quantum Calogero-Moser-Sutherland models, including their relativistic generalizations due to Ruijsenaars and van Diejen, and the relations of these models to classes of special functions developed and explored in recent and on-going research efforts. We give an introduction to these models and corresponding special functions aimed at non-experts. We also describe a few open problems in the field.