Ariznabarreta, GerardoMañas, Manuel2016-07-202016-11-012014-10-20Advances in Mathematics, 2014, v. 264, pp. 396-463https://hdl.handle.net/10016/23388of Toda-like integrable systems are connected us-ing the Gauss-Borel factorization of two, left and a right, Cantero-Morales-Velázquez block moment matrices, which are constructed using a quasi-definite matrix measure. Ablock Gauss-Borel factorization problem of these moment matrices leads to two sets of biorthogonal matrix orthogonal Laurent polynomials and matrix Szegő polynomials, which can be expressed in terms of Schur complements of bordered trun-cations of the block moment matrix. The corresponding block extension of the Christoffel-Darboux theory is derived. De-formations of the quasi-definite matrix measure leading to integrable systems of Toda type are studied. The integrable theory is given in this matrix scenario; wave and adjoint wave functions, Lax and Zakharov-Shabat equations, bilinear equa-tions and discrete flows-connected with Darboux transformations. We generalize the integrable flows of the Cafasso’s matrix extension of the Toeplitz lattice for the Verblunsky coefficients of Szegő polynomials. An analysis of the Miwa shifts allows for the finding of interesting connections between Christoffel-Darboux kernels and Miwa shifts of the matrix orthogonal Laurent polynomials69application/pdfeng© Elsevier 2014Atribución-NoComercial-SinDerivadas 3.0 EspañaMatrix orthogonal Laurent polynomialsBorel-Gauss factorizationChristoffel-Darboux kernelsToda type integrable hierarchiesresearch articleMatemáticasopen access396463Advances in Mathematics264