Tight monomials for quantum enveloping algebras of rank-2 Kac–Moody Lie algebras

The global crystal basis or canonical basis plays an important role in the theory of the quantum groups and their representations. The tight monomials are the simplest elements in the canonical basis. Based on works of Reineke (2001) [11], and Deng and Du (2010) [2], the tight monomials in quantized enveloping algebra associated with Kac–Moody Lie algebras g(C) where are completely determined in this paper.