Spherical orbits and representations of Uε(g)

الأصل · EN

Let Uε(g) be the simply connected quantized enveloping algebra associated to a finite-dimensional complex simple Lie algebra g at the roots of unity. The De Concini-Kac-Procesi conjecture on the dimension of the irreducible representations of Uε(g) is proved for representations corresponding to the spherical conjugacy classes of the simply connected algebraic group G with Lie algebra g. We achieve this result by means of a new characterization of the spherical conjugacy classes of G in terms of elements of the Weyl group.