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

Abstract

In this article, we give two new realizations of the crystal base B(∞) of the negative part 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.