Mod-pReduction for Quantum Groups

AbstractLet Uϵ(G) be the quantized enveloping algebra associated to the Lie algebra G=sl(n+1) at apth-root of unity ε and assume thatpis a prime which does not dividen+1. It is known that the irreducible, finite dimensional representations of Uε(G) are parametrized, up to isomorphisms, by the conjugacy classes of SL(n+1). In the paper we prove that the dimension of any Uε(G)-moduleMparametrized by a conjugacy class O is divided byp1/2dim(O). This result was conjectured by C. De Concini, V. G. Kac, and C. Procesi (J. Amer. Math. Soc.5, 1992, 151–190)