Geodesic
Bethe ansatz and isomondromy deformations
Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 2, pp. 252-265 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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D. V. Talalaev. Bethe ansatz and isomondromy deformations. Teoretičeskaâ i matematičeskaâ fizika, Tome 159 (2009) no. 2, pp. 252-265. http://geodesic.mathdoc.fr/item/TMF_2009_159_2_a5/

[1] D. V. Talalaev, Funkts. analiz i ego pril., 40:1 (2006), 86–91 ; Quantization of the Gaudin system, arXiv: hep-th/0404153 | DOI | MR | Zbl

[2] A. Chervov, D. Talalaev, Quantum spectral curves, quantum integrable systems and the geometric Langlands correspondence, arXiv: hep-th/0604128

[3] E. Mukhin, V. Tarasov, A. Varchenko, The B. and M. Shapiro conjecture in real algebraic geometry and the Bethe ansatz, arXiv: math.AG/0512299 | MR

[4] A. A. Bolibrukh, Fuksovy differentsialnye uravneniya i golomorfnye rassloeniya, MTsNMO, M., 2000 | MR

[5] U. Muğan, A. Sakka, J. Math. Phys., 36:3 (1995), 1284–1298 | DOI | MR | Zbl

[6] K. Iwasaki, H. Kimura, S. Shimomura, M. Yoshida, From Gauss to Painlevé. A Modern Theory of Special Functions, Aspects Math., E16, Vieweg, Brauncschweig, 1991 | DOI | MR | Zbl

[7] E. Frenkel, Bull. Amer. Math. Soc. (N.S.), 41:2 (2004), 151–184 ; arXiv: math.AG/0303074 | DOI | MR | Zbl

[8] A. Gerasimov, D. Lebedev, S. Oblezin, Comm. Math. Phys., 284:3 (2008), 867–896 ; ; On Baxter $Q$-operators and their arithmetic implications, arXiv: 0706.3476arXiv: 0711.2812 | DOI | MR | Zbl