Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discrete Schlesinger Transformations, their Hamiltonian Formulation, and
  Difference Painlev\'e Equations   Schlesinger transformations are algebraic transformations of a Fuchsian
system that preserve its monodromy representation and act on the characteristic
indices of the system by integral shifts. One of the important reasons to study
such transformations is the relationship between Schlesinger transformations
and discrete Painlev\'e equations; this is also the main theme behind our work.
We derive \emph{discrete Schlesinger evolution equations} describing discrete
dynamical systems generated by elementary Schlesinger transformations and give
their discrete Hamiltonian description w.r.t.~the standard symplectic structure
on the space of Fuchsian systems. As an application, we compute explicitly two
examples of reduction from Schlesinger transformations to difference Painlev\'e
equations. The first example, d-$P\big(D_{4}^{(1)}\big)$ (or difference
Painlev\'e V), corresponds to B\"acklund transformations for continuous
$P_{\text{VI}}$. The second example, d-$P\big(A_{2}^{(1)*}\big)$ (with the
symmetry group $E_{6}^{(1)}$), is purely discrete. We also describe the role
played by the geometry of the Okamoto space of initial conditions in comparing
different equations of the same type.

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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: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: eess
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: cs
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The categories of this paper are: physics