  We analyze the large degree asymptotic behavior of matrix valued orthogonal
polynomials (MVOPs), with a weight that consists of a Jacobi scalar factor and
a matrix part. Using the Riemann-Hilbert formulation for MVOPs and the
Deift-Zhou method of steepest descent, we obtain asymptotic expansions for the
MVOPs as the degree tends to infinity, in different regions of the complex
plane (outside the interval of orthogonality, on the interval away from the
endpoints and in neighborhoods of the endpoints), as well as for the matrix
coefficients in the three-term recurrence relation for these MVOPs. The
asymptotic analysis follows the work of Kuijlaars, McLaughlin, Van Assche and
Vanlessen on scalar Jacobi-type orthogonal polynomials, but it also requires
several different factorizations of the matrix part of the weight, in terms of
eigenvalues/eigenvectors and using a matrix Szeg\H{o} function. We illustrate
the results with two main examples, MVOPs of Jacobi and Gegenbauer type, coming
from group theory.

Classical Analysis and ODEs