Transformation Groups

, Volume 10, Issue 1, pp 29–62

Spherical orbits and representations of Uε(g)

Article

DOI: 10.1007/s00031-005-1002-z

Cite this article as:
Cantarini, N., Carnoval, G. & Costantini, M. Transformation Groups (2005) 10: 29. doi:10.1007/s00031-005-1002-z

Abstract

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.

Copyright information

© Birkhauser Boston 2005

Authors and Affiliations

  1. 1.Dipartimento di Matematica, Pura ed Applicata, Universita di Padova, PadovaItaly