Schlesinger transformations for elliptic isomonodromic deformations

Abstract

Schlesinger transformations are discrete monodromy preserving symmetry transformations of the classical Schlesinger system. Generalizing well-known results from the Riemann sphere we construct these transformations for isomonodromic deformations on genus one Riemann surfaces. Their action on the system's tau-function is computed and we obtain an explicit expression for the ratio of the old and the transformed tau-function.

19 pages, LaTeX2e

References in corpus (3)

• Integrable Fredholm Operators and Dual Isomonodromic Deformations
• Gaudin Model, KZ Equation, and Isomonodromic Problem on Torus
• Knizhnik-Zamolodchikov-Bernard equations as a quantization of nonstationary Hitchin system

Cited by in corpus (8)

• On factorized Lax pairs for classical many-body integrable systems
• Isomonodromic tau functions on a torus as Fredholm determinants, and charged partitions
• New contiguity relation of the sixth Painlevé equation from a truncation
• Gaudin models with ${\CU}_q(\mathfrak{osp}(1 | 2))$ symmetry
• Spectral curve and Hamiltonian structure of isomonodromic SU(2) Calogero-Gaudin system
• Discrete symmetries of isomonodromic deformations of order two Fuchsian differential equations
• Circular quiver gauge theories, isomonodromic deformations and $W_N$ fermions on the torus
• The Schlesinger system and isomonodromic deformations of bundles with connections on Riemann surfaces