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

Anton Dzhamay

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

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.

Original languageEnglish
Article number454008
JournalJournal of Physics A: Mathematical and Theoretical
Volume42
Issue number45
DOIs
Publication statusPublished - 2009
Externally publishedYes

Fingerprint

Dive into the research topics of 'Factorizations of rational matrix functions with application to discrete isomonodromic transformations and difference Painlevé equations'. Together they form a unique fingerprint.

Cite this