Relation of Semi-Classical Orthogonal Polynomials to General Schlesinger systems via Twistor Theory
Relation of Semi-Classical Orthogonal Polynomials to General Schlesinger systems via Twistor Theory
复制标题
通过 Twistor 理论半经典正交多项式与一般施莱辛格系统的关系
DOI：
10.1007/978-3-319-52842-7_12
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Hironobu Kimura
中科院分区：
文献类型：
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作者：
Akihito Ebisu and Katsunori Iwasaki;Hironobu Kimura
本文研究了半经典正交多项式与由线性微分方程组的等单点变形而产生的非线性微分方程之间的关系，已有许多工作建立了Painlevé方程与半正交多项式之间的这种关系，其权函数取自超几何积分、库默积分、Bessel积分、Hermite积分、Airy积分的被积函数。对于权函数来自Grassmannian G2，N上的一般超几何积分的半经典正交多项式，得到了这些结果的某些推广。为了建立所需的关系，我们利用Atiyah-Ward Ancestor构造了2 × 2 Schlesinger系统及其退化系统的特解。
We study the relation between semi-classical orthogonal polynomials and nonlinear differential equations coming from the isomonodromic deformation of linear system of differential equations on. There are many works establishing this kind of relations between the Painlevé equations and semi-orthogonal polynomials with the weight functions taking from the integrands for hypergeometric, Kummer, Bessel, Hermite, Airy integrals. Some extension of these results is obtained for the semi-classical orthogonal polynomials with the weight functions coming from the general hypergeometric integrals on the GrassmannianG2,N. To establish the desired relations, we make use of the Atiyah-Ward Ansatz construction of particular solutions for the 2 × 2 Schlesinger system and its degenerated ones.