Let be a bi-homomorphism over an algebraically closed field of characteristic zero. Let U(\chi)) be a generalized quantum group, associated with , such that dimU^+(\chi) = \infty, , and is irreducible, where is the positive part of , and is the Kharchenko positive root system of . In this paper, we give a list of finite-dimensional irreducible -modules, relying on a special reduced expression of the longest element of the Weyl groupoid of . From the list, we explicitly obtain lists of finite-dimensional irreducible modules for simple Lie superalgebras of types A–G and the (standard) quantum superalgebras . An intrinsic gap appears between the lists for and , e.g, if is B or D.
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Saeid Azam, Hiroyuki Yamane, Malihe Yousofzadeh, Classification of Finite-Dimensional Irreducible Representations of Generalized Quantum Groups via Weyl Groupoids. Publ. Res. Inst. Math. Sci. 51 (2015), no. 1, pp. 59–130