Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Schlesinger transformations and quantum R-matrices   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.

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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: math
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: cs