Factorizations of rational matrix functions with application to discrete isomonodromic transformations and difference Painlevé equations

Anton Dzhamay

Результат исследований: Вклад в журналСтатьярецензирование

1 Цитирования (Scopus)

Аннотация

We study factorizations of rational matrix functions with simple poles on the Riemann sphere. For the quadratic case (two poles) we show, using multiplicative representations of such matrix functions, that a good coordinate system on this space is given by a mix of residue eigenvectors of the matrix and its inverse. Our approach is motivated by the theory of discrete isomonodromic transformations and their relationship with difference Painlevé equations. In particular, in these coordinates, basic isomonodromic transformations take the form of the discrete Euler-Lagrange equations. Secondly we show that dPV equations, previously obtained in this context by D Arinkin and A Borodin, can be understood as simple relationships between the residues of such matrices and their inverses.

Язык оригиналаАнглийский
Номер статьи454008
ЖурналJournal of Physics A: Mathematical and Theoretical
Том42
Номер выпуска45
DOI
СостояниеОпубликовано - 2009
Опубликовано для внешнего пользованияДа

Fingerprint

Подробные сведения о темах исследования «Factorizations of rational matrix functions with application to discrete isomonodromic transformations and difference Painlevé equations». Вместе они формируют уникальный семантический отпечаток (fingerprint).

Цитировать