Multi-pole extension for elliptic models of interacting integrable tops

TL;DR

This paper reviews and extends elliptic Gaudin models related to integrable tops, introducing generalizations via R-matrices and connecting them to Schlesinger systems, enriching the mathematical framework of integrable systems.

Contribution

It provides a detailed description of ${ m gl}_{NM}$ Gaudin models, introduces their generalizations using R-matrices, and extends these models to Schlesinger systems, advancing the theory of integrable models.

Findings

Detailed description of ${ m gl}_{NM}$ Gaudin models.

Introduction of models via R-matrices satisfying associative Yang-Baxter.

Extension of models to Schlesinger systems.

Abstract

We review and give detailed description for ${\rm gl}_{NM}$ Gaudin models related to holomorphic vector bundles of rank $NM$ and degree $N$ over elliptic curve with $n$ punctures. Then we introduce their generalizations constructed by means of $R$-matrices satisfying the associative Yang-Baxter equation. A natural extension of the obtained models to the Schlesinger systems is given as well.