Matrix biorthogonal polynomials on the unit circle and non-Abelian Ablowitz-Ladik hierarchy
arXiv:0804.3572 · doi:10.1088/1751-8113/42/36/365211
Abstract
Adler and van Moerbeke \cite{AVM} described a reduction of 2D-Toda hierarchy called Toeplitz lattice. This hierarchy turns out to be equivalent to the one originally described by Ablowitz and Ladik \cite{AL} using semidiscrete zero-curvature equations. In this paper we obtain the original semidiscrete zero-curvature equations starting directly from the Toeplitz lattice and we generalize these computations to the matrix case. This generalization lead us to the semidiscrete zero-curvature equations for the non-abelian (or multicomponent) version of Ablowitz-Ladik equations \cite{GI}. In this way we extend the link between biorthogonal polynomials on the unit circle and Ablowitz-Ladik hierarchy to the matrix case.
23 pages, accepted on publication on J. Phys. A., electronic link: http://stacks.iop.org/1751-8121/42/365211
References in corpus (1)
Cited by in corpus (11)
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