Spherical orbits and quantized enveloping algebras

Let lbe an odd integerl>1 and let ? be a primitive l^th -root of unity. In this paper we prove that every U_?(sl(n))-irreducible module parametrized by a spherical, unipotent conjugacy class О of SL(n) has dimension divisible by l ^½dimОresuit was conjectured by De Concini, Kac and Procesi in [DC-K-P 1].