Abstract
In the present work we investigate the group structure of the Schlesinger transformations for isomonodromic deformations of the Fuchsian differential equations. We perform these transformations as isomorphisms between the moduli spaces of the logarithmic sl(N)-connections with fixed eigenvalues of the residues at singular points. We give a geometrical interpretation of the Schlesinger transformations and perform our calculations using the techniques of the modifications of bundles with connections, or, the Hecke correspondences for the loop group SL(N)⊗C(z).
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References
L. Schlesinger: J. Reine Angew. Math. 141 (1912) 96.
M. Jimbo and T. Miwa: Physica D 2 (1981) 407.
A. Bolibruch: Trudy Matem. Inst. Steklova, Vol. 206, 1994.
N. Hitchin: J. Di. Geom. 3 (1995) 52.
D. Arinkin and S. Lysenko: Math. Res. Lett. 4 (1997) 181.
E. Hecke: Mathematische Werke, Göttingen, 1953.
A. Weil: J. Math. Pure. Appl. (IX) 17 (1938) 47.
V. Drinfeld: in Proc. Int. Cong. Math., Helsinki 1978, Acad. Scient. Fennica, 1980, p. 565.
I. Krichever: Commun. Math. Phys. 229 (2002) 229.
A.M. Levin, M.A. Olshanetsky, and A. Zotov: Commun. Math. Phys. 236 (2003)93.
V. Vakulenko: Preprint in arXiv[xxx.lanl.gov] QA/9909079, 1999.
B. Enriques and V. Rustov: Preprint in arXiv[xxx.lanl.gov] AG/9911087, 1999.
E. Sklyanin: Zapiski Nauch. Sem. LOMI 164 (1987) 151.
E. Sklyanin: Progr. Phys. Suppl. 118 (1995) 35.
S. Oblezin: in Problems of Fundamental and Applied Mathematics, Moscow Institute of Physics and Technology, 2003, p. 61 (in Russian).
H. Bateman and A. Erdélyi: Higher transcendental functions, Vol. 1, 2, McGraw-Hill, 1953.
K. Heun: Math. Annalen XXXIII (1889) 161; 180. 1092 Czech. J. Phys. 53 (2003)
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Oblezin, S. Discrete Structure of Some Schlesinger Systems on the Riemann Sphere. Czechoslovak Journal of Physics 53, 1085–1092 (2003). https://doi.org/10.1023/B:CJOP.0000010538.95492.86
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DOI: https://doi.org/10.1023/B:CJOP.0000010538.95492.86