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

Jeong Ah Kim, Dong Uy Shin

Research output: Contribution to journalArticlepeer-review

Abstract

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)).

Original languageEnglish
Article number111703
JournalJournal of Mathematical Physics
Volume60
Issue number11
DOIs
StatePublished - 2019 Nov 1

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