  Using the representation theory of sl(2) and an appropriate model for tensor
product of lowest weight Verma modules, we give a realisation first of the Hahn
algebra, and then of the Racah algebra, using Jacobi differential operators.
While doing so we recover some known convolution formulas for Jacobi
polynomials involving Hahn and Racah polynomials. Similarly, we produce
realisations of the higher rank Racah algebras in which maximal commutative
subalgebras are realised in terms of Jacobi differential operators.
