Zigzag strip bundles and crystals

We introduce new combinatorial models, called zigzag strip bundles, over quantum affine algebras U q ( B n ( 1 ) ) , U q ( D n ( 1 ) ) and U q ( D n + 1 ( 2 ) ) , and show that the sets of all zigzag strip bundles for U q ( B n ( 1 ) ) , U q ( D n ( 1 ) ) and U q ( D n + 1 ( 2 ) ) realize the crystal bases B ( ∞ ) of U q − ( B n ( 1 ) ) , U q − ( D n ( 1 ) ) and U q − ( D n + 1 ( 2 ) ) , respectively. Further, we discuss the connection between zigzag strip bundle realization, Nakajima monomial realization, and polyhedral realization of the crystal B ( ∞ ) .