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 $M$ 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.

arXiv comment25 pages, minor changes, typos corrected

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Cited by in corpus (3)

• 2d Integrable systems, 4d Chern-Simons theory and Affine Higgs bundles
• Lax equations for relativistic $\mathrm{GL}(NM,\mathbb{C})$ Gaudin models on elliptic curve
• Integrable systems on multiplicative quiver varieties from cyclic quivers