Matrix valued orthogonal polynomials related to SU$(N+1)$, their algebras of differential operators and the corresponding curves

TL;DR

This paper explores matrix valued orthogonal polynomials linked to SU(N+1), presenting two examples of differential operator algebras—one commutative and one non-commutative—derived from group representations.

Contribution

It introduces two specific algebras of differential operators associated with matrix valued orthogonal polynomials from SU(N+1) representations, highlighting their algebraic structures.

Findings

One algebra is commutative, the other is non-commutative.

Examples are explicitly constructed from SU(N+1) representations.

The work connects group representations with differential operator algebras.

Abstract

We give two examples of algebras of differential operators associated to families of matrix valued orthogonal polynomials arising from representations of SU$(N+1)$. The first one gives a commutative algebra and the second one a non--commutative one.