We generalize a criterion for tight monomials of quantum enveloping algebras associated with symmetric generalized Cartan matrices and a monomial basis property of those associated with symmetric (classical) Cartan matrices to their respective symmetrizable case. We then link the two by establishing that a tight monomial is necessarily a monomial defined by a weakly distinguished word. As an application, we develop an algorithm to compute all tight monomials in the rank 2 Dynkin case. © 2010 Elsevier Inc.
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