ADDITION FORMULA FOR Q-DISK POLYNOMIALS

Explicit models are constructed for irreducible -representations of t he quantised universal enveloping algebra U-q(gl(n)). The irreducible decomposition of these modules with respect to the subalgebra U,(gl(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, t he so-called q-disk polynomials.