Verma and simple modules for quantum groups at non-abelian groups
Abstract
The Drinfeld double D of the bosonization of a finite-dimensional Nichols algebra B(V) over a finite non-abelian group G is called a quantum group at a non-abelian group. We introduce Verma modules over such a quantum group D and prove that a Verma module has simple head and simple socle. This provides two bijective correspondences between the set of simple modules over D and the set of simple modules over the Drinfeld double D(G). As an example, we describe the lattice of submodules of the Verma modules over the quantum group at the symmetric group S3 attached to the 12-dimensional Fomin-Kirillov algebra, computing all the simple modules and calculating their dimensions.
Cite
@article{arxiv.1409.0438,
title = {Verma and simple modules for quantum groups at non-abelian groups},
author = {Barbara Pogorelsky and Cristian Vay},
journal= {arXiv preprint arXiv:1409.0438},
year = {2016}
}
Comments
29 pages, 4 figures v2: final version. Main changes: Theorem 5 is new and Sections 4.3, 4.4, 4.5 and 4.5 were improved