Induced conjugacy classes and induced U_e(G)-modules
Abstract
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.
Keywords
Cite
@article{arxiv.1210.0237,
title = {Induced conjugacy classes and induced U_e(G)-modules},
author = {Giovanna Carnovale},
journal= {arXiv preprint arXiv:1210.0237},
year = {2012}
}
Comments
This paper is an expanded version of a lecture given at the conference "Hopf algebras and tensor categories", Almeri'a, July 2011. It will appear in the volume of Contemporary Math. containing the conference Proceedings