Relativistic interacting integrable elliptic tops

Abstract

We propose relativistic generalization of integrable systems describing $M$ interacting elliptic $\mathrm{gl}(N)$ tops of the Euler-Arnold type. The obtained models are elliptic integrable systems, which reproduce the spin elliptic $\mathrm{GL}(M)$ Ruijsenaars-Schneider model for $N=1$ case, while in the $M=1$ case they turn into relativistic integrable $\mathrm{GL}(N)$ elliptic tops. The Lax pairs with spectral parameter on elliptic curve are constructed.

17 pages

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Cited by in corpus (6)

• Anisotropic spin generalization of elliptic Macdonald-Ruijsenaars operators and R-matrix identities
• Elliptic generalization of integrable q-deformed anisotropic Haldane-Shastry long-range spin chain
• Integrable System of Generalized Relativistic Interacting Tops
• Lax equations for relativistic $\mathrm{GL}(NM,\mathbb{C})$ Gaudin models on elliptic curve
• Quadratic algebras based on SL(NM) elliptic quantum R-matrices
• On R-matrix identities related to elliptic anisotropic spin Ruijsenaars-Macdonald operators