論文

2017年1月1日

Relation of semi-classical orthogonal polynomials to general schlesinger systems via twistor theory

Trends in Mathematics
  • Hironobu Kimura

開始ページ
399
終了ページ
414
DOI
10.1007/978-3-319-52842-7_12

© Springer International Publishing AG 2017. 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 P1. There aremany 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 Grassmannian G2,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.

リンク情報
DOI
https://doi.org/10.1007/978-3-319-52842-7_12
Scopus
https://www.scopus.com/record/display.uri?eid=2-s2.0-85022057445&origin=inward
URL
https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85022057445&origin=inward