  A ladder structure of operators is presented for the Jacobi polynomials,
J_n^(a,b)(x), with parameters n, a and b integers, showing that they are
related to the unitary irreducible representation of SU(2,2) with quadratic
Casimir C_SU(2,2)=-3/2. As they determine also a base of square-integrable
functions, the universal enveloping algebra of su(2,2) is homomorphic to the
space of linear operators acting on the L^2 functions defined on (-1,+1) x Z x
Z/2.
