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Schlesinger transformations and quantum R-matrices | | N. Manojlovic
; H. Samtleben
; | | Date: |
10 Dec 2001 | | Journal: | Commun.Math.Phys. 230 (2002) 517-537 | | Subject: | Exactly Solvable and Integrable Systems | nlin.SI hep-th | | Abstract: | 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. | | Source: | arXiv, nlin.SI/0112016 | | Services: | Forum | Review | PDF | Favorites | |
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