Complex hypergeometric functions and integrable many-body problems

TL;DR

This paper explores the reduction of elliptic hypergeometric equations to complex hypergeometric functions and introduces new rational integrable many-body systems derived from degenerations of known models.

Contribution

It presents a general reduction method for elliptic hypergeometric equations and introduces new integrable N-body systems from degenerations of elliptic models.

Findings

Reduction of elliptic hypergeometric equations to complex hypergeometric functions

Derivation of new rational integrable N-body systems

Connection to degenerations of elliptic Ruijsenaars and van Diejen models

Abstract

General reduction of the elliptic hypergeometric equation to the level of complex hypergeometric functions is described. The derived equation is generalized to the Hamiltonian eigenvalue problem for new rational integrable $N$-body systems emerging from particular degenerations of the elliptic Ruijsenaars and van Diejen models.