Multi-pole extension for elliptic models of interacting integrable tops

Abstract

We review and give detailed description for ${\mathrm{gl}}_{NM}$ 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.

25 pages, minor changes

References in corpus (5)

• Relativistic Classical Integrable Tops and Quantum R-matrices
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• Characteristic Classes and Integrable Systems for Simple Lie Groups
• Characteristic Classes and Integrable Systems. General Construction
• Hecke Transformations of Conformal Blocks in WZW Theory. I. KZB Equations for Non-Trivial Bundles