Zigzag strip bundles and highest weight crystals

Abstract Zigzag strip bundles are new combinatorial models realizing the crystals B ( ∞ ) for the quantum affine algebras U q ( g ) , where g = B n ( 1 ) , D n ( 1 ) , D n + 1 ( 2 ) , C n ( 1 ) , A 2 n − 1 ( 2 ) , A 2 n ( 2 ) . In this paper, we give new realizations of the crystal bases B ( λ ) for the irreducible highest weight modules V ( λ ) over quantum affine algebras U q ( g ) using zigzag strip bundles. Further, we discuss the connection between zigzag strip bundle realization, Nakajima monomial realization, and polyhedral realization of the crystals B ( λ ) .