The authors start with the Casimir operator, i.e., more precisely, a differential operator acting on matrix-valued functions on the group \(\text{SU}(N+1)\), and derive certain ordinary differential operators on the interval \([0,1]\) acting on matrix-valued functions. In this way, the authors present two examples of algebras of differential operators associated with orthogonal polynomials arising from representations of \(\text{SU}(N+1)\). The one-step example here is commutative, while the second example with two steps is noncommutative.