Classification of Finite Dimensional Irreducible Representations of Generalized Quantum Groups via Weyl Groupoids

Abstract

We classify finite-dimensional irreducible highest weight modules of generalized quantum groups whose positive part is infinite dimensional and has a Kharchenko's PBW basis with an irreducible finite positive root system.

59 pages, We give and prove some reduced expressions of the longest elements of not only the Weyl groupoids treated in the paper, but also the finite Weyl groups