Addition formula for q-disk polynomials

Abstract. Explicit models are constructed for irreducible *-representations of the quantised universalenveloping algebra Uq(gl(n)). The irreducible decomposition of these modules with respect to thesubalgebra Uq(gl(n-1)) is given, and the corresponding spherical and associated spherical elementsare determined in terms of little q-Jacobi polynomials. This leads to a proof of an addition theoremfor the spherical elements, the so-called q-disk polynomials.