Quantized universal enveloping algebras at the roots of unity and spherical conjugacy classes
by
Giovanna Carnovale
University of Padua, Italy
Coauthors: Nicoletta Cantarini, Mauro Costantini

Let U_\epsilon(g) be the simply connected quantized enveloping algebra associated to a simple Lie algebra g at the roots of unity. There exists a natural map from the set of irreducible representations of U_\epsilon(g) to the set of conjugacy classes of the simply connected algebraic group G with Lie algebra g. A conjecture of De Concini, Kac and Procesi relates the possible dimensions of irreducible representations of U_\epsilon(g) to the dimension of the corresponding conjugacy classes. We prove the De Concini, Kac and Procesi conjecture for representations associated to spherical conjugacy classes. The case of a Lie algebra of type A_n had been handled by N. Cantarini.

Date received: April 17, 2003

Copyright © 2003 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caju-56.