论文标题
Cauchy Bi-Ottrodonal多项式和可整合晶格的两参数概括
Two-parameter generalisations of Cauchy bi-orthogonal polynomials and integrable lattices
论文作者
论文摘要
在本文中，我们考虑了广义的两参数Cauchy两矩阵模型和相应的可集成晶格方程。 It is shown that with parameters chosen as $1/k_i$ when $k_i\in\mathbb{Z}_{>0}$ ($i=1,\,2$), the average characteristic polynomials admit $(k_1+k_2+2)$-term recurrence relations, which provide us spectral problems for integrable lattices.然后，tau函数由广义的cauchy两矩阵模型的分区函数以及克决定因素给出。展示了具有精确溶解性的最简单示例。
In this article, we consider the generalised two-parameter Cauchy two-matrix model and corresponding integrable lattice equation. It is shown that with parameters chosen as $1/k_i$ when $k_i\in\mathbb{Z}_{>0}$ ($i=1,\,2$), the average characteristic polynomials admit $(k_1+k_2+2)$-term recurrence relations, which provide us spectral problems for integrable lattices. The tau function is then given by the partition function of the generalised Cauchy two-matrix model as well as Gram determinant. The simplest example with exact solvability is demonstrated.
