QUANTUM SUPERGROUPS I. FOUNDATIONS

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.