Integrable structures of specialized hypergeometric tau functions (Mathematical structures of integrable systems, its deepening and expansion)

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Description

Okounkov's generating function of the double Hurwitz numbers of the Riemann sphere is a hypergeometric tau function of the 2D Toda hierarchy in the sense of Orlov and Scherbin. This tau function turns into a tau function of the lattice KP hierarchy by specializing one of the two sets of time variables to constants. When these constants are particular values, the specialized tau functions become solutions of various reductions of the lattice KP hierarchy, such as the lattice Gelfand-Dickey hierarchy, the Bogoyavlensky-Itoh-Narita lattice and the Ablowitz-Ladik hierarchy. These reductions contain previously unknown integrable hierarchies as well.

Journal

  • RIMS Kokyuroku Bessatsu

    RIMS Kokyuroku Bessatsu B87 57-78, 2021-08

    Research Institute for Mathematical Sciences, Kyoto University

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Details 詳細情報について

  • CRID
    1050852945208878080
  • NII Article ID
    120007167310
  • NII Book ID
    AA12196120
  • HANDLE
    2433/265828
  • ISSN
    18816193
  • Text Lang
    en
  • Article Type
    departmental bulletin paper
  • Data Source
    • IRDB
    • CiNii Articles

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