  In this paper, we study parameter deformations of matrix valued orthogonal
polynomials (MVOPs). These deformations are built on the use of certain matrix
valued operators which are symmetric with respect to the matrix valued inner
product defined by the orthogonality weight. We show that the recurrence
coefficients associated with these operators satisfy generalizations of the
non-Abelian lattice equations. We provide a Lax pair formulation for these
equations, and an example of deformed Hermite-type matrix valued polynomials is
discussed in detail.
