This article is cited in 2 papers

Degenerating the elliptic Schlesinger system

G. Aminov, S. Arthamonov

Moscow Institute of Physics and Technology , Moscow, Russia

Abstract: We study various ways of degenerating the Schlesinger system on the elliptic curve with $R$ marked points. We construct a limit procedure based on an infinite shift of the elliptic curve parameter and on shifts of the marked points. We show that using this procedure allows obtaining a nonautonomous Hamiltonian system describing the Toda chain with additional spin $\mathfrak{sl}(N,\mathbb C)$ degrees of freedom.

Keywords: integrable system, isomonodromic deformation, Schlesinger system, Toda chain, Inozemtsev limit.

DOI: 10.4213/tmf8375

 English version: Theoretical and Mathematical Physics, 2013, 174:1, 1–20

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