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TMF, 2009 Volume 159, Number 2, Pages 252–265 (Mi tmf6346)

Bethe ansatz and isomondromy deformations

D. V. Talalaev

Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)

Abstract: We study symmetries of the Bethe equations for the Gaudin model. These symmetries arise naturally under the name Hecke operator in the framework of the geometric Langlands correspondence and under the name Schlesinger transformation in the theory of isomondromy deformations, in particular, in the theory of Painlevé transcendents.

Keywords: Gaudin model, Bethe ansatz, isomondromy transformation.

DOI: 10.4213/tmf6346


 English version:
Theoretical and Mathematical Physics, 2009, 159:2, 627–639

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© Steklov Math. Inst. of RAS, 2024