Factorizations of Rational Matrix Functions with Application to Discrete Isomonodromic Transformations and Difference Painlevé Equations - Mathematical PhysicsReportar como inadecuado




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Abstract: We study factorizations of rational matrix functions with simple poles on theRiemann sphere. For the quadratic case two poles we show, usingmultiplicative representations of such matrix functions, that a good coordinatesystem on this space is given by a mix of residue eigenvectors of the matrixand its inverse. Our approach is motivated by the theory of discreteisomonodromic transformations and their relationship with difference Painlev\-eequations. In particular, in these coordinates, basic isomonodromictransformations 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 theresidues of such matrices and their inverses.



Autor: Anton Dzhamay

Fuente: https://arxiv.org/



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