Jacobi Polynomials as su(2, 2) Unitary Irreducible Representation

An infinite-dimensional irreducible representation of su(2, 2) is explicitly constructed in terms of ladder operators for the Jacobi polynomials \(J_{n}^{({\alpha },\beta )}(x)\) and the Wigner dj-matrices where the integer and half-integer spins j := n + (α + β)∕2 are considered together. The 15 generators of this irreducible representation are realized in terms of zero or first order differential operators and the algebraic and analytical structure of operators of physical interest discussed.