Asymptotics of matrix valued orthogonal polynomials on [−1,1]

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