Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Biorthogonal Laurent polynomials, Toeplitz determinants, minimal Toda
  orbits and isomonodromic tau functions   We consider the class of biorthogonal polynomials that are used to solve the
inverse spectral problem associated to elementary co-adjoint orbits of the
Borel group of upper triangular matrices; these orbits are the phase space of
generalized integrable lattices of Toda type. Such polynomials naturally
interpolate between the theory of orthogonal polynomials on the line and
orthogonal polynomials on the unit circle and tie together the theory of Toda,
relativistic Toda, Ablowitz-Ladik and Volterra lattices. We establish
corresponding Christoffel-Darboux formulae . For all these classes of
polynomials a 2x2 system of Differential-Difference-Deformation equations is
analyzed in the most general setting of pseudo measures with arbitrary rational
logarithmic derivative. They provide particular classes of isomonodromic
deformations of rational connections on the Riemann sphere. The corresponding
isomonodromic tau function is explicitly related to the shifted Toeplitz
determinants of the moments of the pseudo-measure. In particular the results
imply that any (shifted) Toeplitz (Hankel) determinant of a symbol (measure)
with arbitrary rational logarithmic derivative is an isomonodromic tau
function.

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The categories of this paper are: cs
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th