Spherical orbits and representations of Uε(g)
- Cite this article as:
- Cantarini, N., Carnoval, G. & Costantini, M. Transformation Groups (2005) 10: 29. doi:10.1007/s00031-005-1002-z
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Let Uε(g) be the simply connected quantized enveloping algebra at roots of one associated to a finite dimensional complex simple Lie algebra g. The De Concini-Kac-Procesi conjecture on the dimension of the irreducible representations of Uε(g) is proved for the 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.