Multi-pole extension of the elliptic models of interacting integrable tops

We review and give a detailed description of the $gl_{NM}$ Gaudin models related to holomorphic vector bundles of rank $NM$ and degree $N$ over an elliptic curve with $n$ punctures. 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 also given.