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

Motivated by the zigzag strip bundles which are combinatorial models realizing the crystals B(∞) for the quantum affine algebras Uq(g), where g=Bn(1),Dn(1),Dn+1(2),Cn(1), A2n-1(2),A2n(2), we introduce a new combinatorial model called strip bundles for the quantum affine algebra Uq(G2(1)). We give new realizations S(∞) and S(λ) of the crystal B(∞) and the highest weight crystals B(λ) over Uq(G2(1)) using strip bundles, and as subsets of S(∞) and S(λ), we also give realizations of the crystal B(∞) and the highest weight crystals B(λ) over the quantum finite algebra U_q(G₂). Moreover, we give characterizations of the image of the crystal embedding ψ_i and the connected component C1 in the set M of all Nakajima monomials which are isomorphic to the crystal B(∞) over Uq(G2(1)).