Nakajima Monomials, Strip Bundles, and the Crystals B(∞) Over U _q(B _∞), and U _q(C _∞), and U _q(D _∞)

In this article, we give two new realizations of the crystal base B(∞) of the negative part U _q ^-(g) of the quantum generalized Kac-Moody algebra U _q(g) (g = B _∞, C _∞ or D _∞) using Nakajima monomials and strip bundles, respectively. Furthermore, we discuss the relation between monomial realization and strip bundle realization.