Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2001-12-10
Commun.Math.Phys. 230 (2002) 517-537
Nonlinear Sciences
Exactly Solvable and Integrable Systems
22 pages, LaTeX2e
Scientific paper
10.1007/s00220-002-0716-1
Schlesinger transformations are discrete monodromy preserving symmetry transformations of a meromorphic connection which shift by integers the eigenvalues of its residues. We study Schlesinger transformations for twisted sl_N-valued connections on the torus. A universal construction is presented which gives the elementary two-point transformations in terms of Belavin's elliptic quantum R-matrix. In particular, the role of the quantum deformation parameter is taken by the difference of the two poles whose residue eigenvalues are shifted. Elementary one-point transformations (acting on the residue eigenvalues at a single pole) are constructed in terms of the classical elliptic r-matrix. The action of these transformations on the tau-function of the system may completely be integrated and we obtain explicit expressions in terms of the parameters of the connection. In the limit of a rational R-matrix, our construction and the tau-quotients reduce to the classical results of Jimbo and Miwa in the complex plane.
Manojlovic Nenad
Samtleben Henning
No associations
LandOfFree
Schlesinger transformations and quantum R-matrices does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Schlesinger transformations and quantum R-matrices, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Schlesinger transformations and quantum R-matrices will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-140223