Using the theory introduced by Casper and Yakimov, we investigate the structure of algebras of differential and difference operators acting on matrix valued orthogonal polynomials (MVOPs) on $\mathbb{ R}$, and we derive algebraic and differential relations for these MVOPs. A particular case of importance is that of MVOPs with respect to a matrix weight of the form $W(x)=e^{ -v(x)}e^{ xA} e^{ xA^\ast}$ on the real line, where $v$ is a scalar polynomial of even degree with positive leading coefficient and $A$ is a constant matrix.
Categories: math.CA