Quantum Supergroups I. Foundations
Quantum Algebra
2013-11-20 v2 Representation Theory
Abstract
In this part one of a series of papers, we introduce a new version of quantum covering and super groups with no isotropic odd simple root, which is suitable for the studies of integrable modules, integral forms and bar-involution. A quantum covering group involves a quantum parameter q and a sign parameter pi squaring to 1, and it specializes to a quantum supergroup when pi=-1. Following Lusztig, we formulate and establish various structural results of the quantum covering groups, including bilinear form, quasi-R-matrix, Casimir, character formulas for integrable modules, and higher Serre relations.
Keywords
Cite
@article{arxiv.1301.1665,
title = {Quantum Supergroups I. Foundations},
author = {Sean Clark and David Hill and Weiqiang Wang},
journal= {arXiv preprint arXiv:1301.1665},
year = {2013}
}
Comments
v1 30 pages; v2 31 pages, minor corrections and adapted to journal guidelines, to appear in Transformation Groups