Zigzag strip bundles and highest weight crystals

Abstract

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.