Abstract. Explicit models are constructed for irreducible *-representations of the quantised universal enveloping algebra $U_q({\frak g}{\frak l}(n))$. The irreducible decomposition of these modules with respect to the subalgebra $U_q({\frak g}{\frak l}(n-1))$ is given, and the corresponding spherical and associated spherical elements are determined in terms of little $q$-Jacobi polynomials. This leads to a proof of an addition theorem for the spherical elements, the so-called $q$-disk polynomials.
