Zigzag strip bundles and highest weight crystals

Zigzag strip bundles are new combinatorial models realizing the crystals B(infinity) for the quantum affine algebras U-q(g), where g = B-n((1)), D-n((1)), D-n+1((2)), C-n((1)), A(2n-1)((2)), A(2n)((2)). In this paper, we give new realizations of the crystal bases B(lambda) for the irreducible highest weight modules V(lambda) 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(lambda). (C) 2014 Elsevier Inc. All rights reserved.The first author's research was supported by NRF Grant # 2012 R1A1A3013924. The second author's research was supported by KOSEF Grant #2009-00688200