Elliptic Schlesinger system and Painlevé VI

Journal of Physics A: Mathematical and General

Volumn 39, Issue 39, 2006, Pages 12083-12101

  Chernyakov, Yu ^a   Levin, A M ^b,c   Olshanetsky, M ^a,c,d   Zotov, A ^a  

^a INSTITUTE FOR THEORETICAL AND EXPERIMENTAL PHYSICS   (Russian Federation)

^b SHIRSHOV INSTITUTE OF OCEANOLOGY   (Russian Federation)

^c MAX PLANCK INSTITUT FÜR MATHEMATIK   (Germany)

^d LEIBNIZ UNIVERSITY HANNOVER   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33748786542     PISSN: 03054470     EISSN: 13616447     Source Type: Journal    
DOI: 10.1088/0305-4470/39/39/S05     Document Type: Article

References (21)

1. Schlesinger L 1912 ber eine Klasse von Differentialsystemen beliebeger Ordnung mit fersten kritischen Punkten J. Reine Angew. Math. 141 96-145
2. Jimbo M, Miwa T and Ueno K 1981 Monodromy preserving deformations of linear ordinary differential equations: I Physica D 2 306-52
3. Jimbo M, Miwa T and Ueno K 1981 Monodromy preserving deformations of linear ordinary differential equations: II Physica D 2 407-48
4. Okamoto K 1986 Isomonodromic deformation and the Painlevé equations and the Garnier system J. Fac. Sci. Univ. Tokyo IA 33 575-618
5. Kitaev A and Korotkin D 1998 On solutions of the Schlesinger equations in terms of Θ-functions Int. Math. Res. Not. 17 877-905
6. Takasaki K 1998 Gaudin model, KZ equation, and isomonodromic deformation on torus Lett. Math. Phys. 44 143-56 (Preprint hep-th/9711058)
7. Levin A and Olshanetsky M 1999 Hierarchies of isomonodromic deformations and Hitchin systems Moscow Seminar in Mathematical Physics (Am. Math. Soc. Transl. Ser. 2) vol 191 (Providence, RI: American Mathematical Society) pp 223-62 (Preprint hep-th/9709207)
8. Reyman A and Semenov-Tyan-Shansky A G M 1991 Group-theoretical methods in the theory of finite-dimensional integrable systems Encyclopedia of Mathematical Science vol 16 (Berlin: Springer) pp 116-225
9. Sklyanin E and Takebe T 1996 Algebraic Bethe ansatz for the XYZ Gaudin model Phys. Lett. A 219
10. Nekrasov N 1996 Holomorphic bundles and many-body systems Commun. Math. Phys. 180 587-604
11. Korotkin D and Samtleben J A H 1997 On the quantization of isomonodromic deformations on the torus Int. J. Mod. Phys. A 12 2013-30 (Preprint hep-th/9511087)
12. Sklyanin E 1982 Some algebraic structures connected with the Yang-Baxter equation Funct. Anal. Appl. 16 27-34
13. Feigin B and Odesski A 1989 Sklyanin's elliptic algebras Funct. Anal. Appl. 23 207-14
14. Levin A, Olshanetsky M and Zotov A 2005 Painlevé VI, rigid tops and reflection equation Preprint math.QA/0508058 (Commun. Math. Phys. submitted)
15. Painlevé P 1906 Sur les équations différentielles du second odre points critics fixes C. R. Acad. Sci., Paris 143 1111-7
16. 2 Geometry of Differential Equations (Am. Math. Soc. Transl. Ser. 2) vol 186 (Providence, RI: American Mathematical Society) pp 131-51
17. Zotov A 2004 Elliptic linear problem for Calogero-Inozemtsev model and Painlevé VI equation Lett. Math. Phys. 67 153-65
18. Krichever I 1994 The tau-function of the universal Whitham hierarchy, matrix models and topological field theories Commun. Pure Appl. Math. 47 437-75
19. Braden H, Dolgushev V, Olshanetsky M and Zotov A 2003 Classical r-matrices and the Feigin-Odesski algebra via Hamiltonian and Poisson reductions J. Phys. A: Math. Gen. 36 6979-7000
20. Belavin A and Drinfeld V 1982 Solutions of the classical Yang-Baxter equation for simple Lie algebras Funct. Anal Appl. 16 1-29
21. Magri F 1978 A simple model for the integrable Hamiltonian equation J. Math. Phys. 19 1156-62