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).