Zigzag strip bundles and crystals

We introduce new combinatorial models, called zigzag strip bundles, over quantum affine algebras , and , and show that the sets of all zigzag strip bundles for , and realize the crystal bases B(∞) of , and , respectively. Further, we discuss the connection between zigzag strip bundle realization, Nakajima monomial realization, and polyhedral realization of the crystal B(∞).