TY - JOUR

T1 - Strip bundle realization of the crystals over U q (G 2 (1))

AU - Kim, Jeong Ah

AU - Shin, Dong Uy

N1 - Publisher Copyright:
© 2019 Author(s).

PY - 2019/11/1

Y1 - 2019/11/1

N2 - 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 Uq(G2). Moreover, we give characterizations of the image of the crystal embedding ψi and the connected component C1 in the set M of all Nakajima monomials which are isomorphic to the crystal B(∞) over Uq(G2(1)).

AB - 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 Uq(G2). Moreover, we give characterizations of the image of the crystal embedding ψi and the connected component C1 in the set M of all Nakajima monomials which are isomorphic to the crystal B(∞) over Uq(G2(1)).

UR - http://www.scopus.com/inward/record.url?scp=85074996287&partnerID=8YFLogxK

U2 - 10.1063/1.5094915

DO - 10.1063/1.5094915

M3 - Article

AN - SCOPUS:85074996287

VL - 60

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 11

M1 - 111703

ER -