Abstract
We give new realizations of the crystal bases of the Verma modules and the irreducible highest weight modules over the quantum generalized Kac–Moody algebra U q (A ∞) and the quantum Monster algebra using Nakajima monomials. Moreover, another realization of the crystals B(∞) and B(λ) over U q (A ∞) using triangular matrices and tableaux are given.
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