Two-parameter Quantum Groups of Exceptional Type E-Series and Convex PBW-type Basis

Abstract

The presentation of two-parameter quantum groups of type E-series in the sense of Benkart–Witherspoon is given, which has a Drinfel'd quantum double structure. The universal R-matrix and a convex PBW-type basis are described for type E6(as a sample), and the conditions of an isomorphism from these quantum groups into the one-parameter quantum doubles are discussed.