块Toeplitz行列式、约束KP和Gelfand-Dickey族
Block Toeplitz determinants, constrained KP and Gelfand-Dickey hierarchies
摘要：
我们提出了一种方法来计算任何Gelfand-Dickey tau函数生活在Segal-Wilson Grassmannian作为块Toeplitz行列式的渐近与某一类别的符号。此外，截断块Toeplitz行列式与相同的符号被证明是τ函数的合理减少KP。本文从可积系统的观点和块Toeplitz算子理论两个方面研究了它与黎曼-希尔伯特问题的联系。代数几何解决方案的应用程序的例子。
英文摘要：
We propose a method for computing any Gelfand-Dickey tau function living in Segal-Wilson Grassmannian as the asymptotics of block Toeplitz determinant associated to a certain class of symbols. Also truncated block Toeplitz determinants associated to the same symbols are shown to be tau function for rational reductions of KP. Connection with Riemann-Hilbert problems is investigated both from the point of view of integrable systems and block Toeplitz operator theory. Examples of applications to algebro-geometric solutions are given.
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