Strip bundle realization of the crystals over U-q(G(2)((1)))

Abstract

Motivated by the zigzag strip bundles which are 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)), we introduce a new combinatorial model called strip bundles for the quantum affine algebra U-q(G(2)((1))). We give new realizations S(infinity) and S(lambda) of the crystal B(infinity) and the highest weight crystals B(lambda) over Uq(G2(1)) using strip bundles, and as subsets of S(infinity) and S(lambda), we also give realizations of the crystal B(infinity) and the highest weight crystals B(lambda) over the quantum finite algebra U-q(G(2)). Moreover, we give characterizations of the image of the crystal embedding Psi(i) and the connected component C(1) in the set M of all Nakajima monomials which are isomorphic to the crystal B(infinity) over U-q(G(2)((1))).