  By work of De Concini, Kac and Procesi the irreducible representations of the
non-restricted specialization of the quantized enveloping algebra of the Lie
algebra g at the roots of unity are parametrized by the conjugacy classes of a
group G with Lie(G)=g. We show that there is a natural dimension preserving
bijection between the sets of irreducible representations associated with
conjugacy classes lying in the same Jordan class (decomposition class). We
conjecture a relation for representations associated with classes lying in the
same sheet of G, providing two alternative formulations. We underline some
evidence and illustrate potential consequences.
