Matrix orthogonality in the plane versus scalar orthogonality in a Riemann surface

Abstract We consider a non-Hermitian matrix orthogonality on contour in the complex plane. Given diagonalizable and rational valued weight, we show that Christoffel–Darboux (CD) kernel, which is built terms of orthogonal polynomials, equivalent to scalar reproducing kernel meromorphic functions Riemann surface. If this surface has genus $0$, then CD polynomials Interestingly, not necessarily kernel. As an application our result, correlation certain doubly periodic lozenge tiling models admits double integral representation involving only This simplifies formula Duits Kuijlaars.