Abstract
We introduce the notion of Nakajima monomials for quantum generalized Kac–Moody algebras and construct the crystals B ( ∞ ) and B ( λ ) in terms of Nakajima monomials. We also give an explicit description of the Nakajima monomials in the crystals B ( ∞ ) and B ( λ ) for the rank 2 quantum generalized Kac–Moody algebras and for the quantum Monster algebra.
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