论文标题
专门的超几何tau功能的集成结构
Integrable structures of specialized hypergeometric tau functions
论文作者
论文摘要
Okounkov的Riemann Sphere的双Hurwitz数量的生成函数是Orlov和Scherbin的意义上的2D TODA层次结构的超几何tau函数。该tau函数通过将两组时间变量之一的一个集合到常数中之一，转化为晶格KP层次结构的tau函数。当这些常数是特定值时，专业的tau函数将成为晶格KP层次结构各种降低的解决方案，例如晶格Gelfand-Dickey层次结构，Bogoyavlensky-Itoh-Narita Lattice和Ablowitz-Ladik层次。这些减少还包含以前未知的集成层次结构。
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.
