QUANTUM SUPERGROUPS I. FOUNDATIONS

被引：0
作者：
Clark S. [1 ]
Hill D. [1 ]
Wang W. [1 ]
机构：
[1] Department of Mathematics, University of Virginia, Charlottesville, VA
来源：
Transformation Groups | 2013年 / 18卷 / 4期
关键词：
Quantum Group; Braid Group; Verma Module; Integrable Module; Character Formula;
D O I：
10.1007/s00031-013-9247-4
中图分类号：
学科分类号：
摘要：
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 study of integrable modules, integral forms, and the bar involution. A quantum covering group involves parameters q and π with π2 = 1, and it specializes at π = -1 to a quantum supergroup. Following Lusztig, we formulate and establish various structural results of the quantum covering groups, including a bilinear form, quasi-R-matrix, Casimir element, character formulas for integrable modules, and higher Serre relations. © 2013 Springer Science+Business Media New York.
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页码：1019 / 1053
页数：34
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