Zigzag Strip Bundle Realization of B(Λ0) over Uq(Cn(1))

Jeong Ah Kim; Dong Uy Shin

doi:10.1007/s10468-016-9624-5

Zigzag Strip Bundle Realization of B(Λ₀) over Uq(Cn(1))

Jeong Ah Kim
, Dong Uy Shin

Department of Mathematics

Hanyang University

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

Zigzag strip bundles are new combinatorial models realizing the crystals B(∞) for the quantum affine algebras U_q(g) , where (g)=Bn(1),Dn(1), Dn+1(2), Cn(1), A2n−1(2), A2n(2). Recently, these models were used to the realization of highest weight crystals except for the highest weight crystal B(Λ₀) over the quantum affine algebra Uq(Cn(1)). In this paper, we construct the highest weight crystal B(Λ₀) over the quantum affine algebra Uq(Cn(1)) using zigzag strip bundles, which completes the realizations of all highest weight crystals over U_q(g).

Original language	English
Pages (from-to)	1423-1436
Number of pages	14
Journal	Algebras and Representation Theory
Volume	19
Issue number	6
DOIs	https://doi.org/10.1007/s10468-016-9624-5
State	Published - 1 Dec 2016

Keywords

Crystals
Kashiwara embeddings
Nakajima monomials
Zigzag strip bundles

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10.1007/s10468-016-9624-5

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title = "Zigzag Strip Bundle Realization of B(Λ0) over Uq(Cn(1))",

abstract = "Zigzag strip bundles are new 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). Recently, these models were used to the realization of highest weight crystals except for the highest weight crystal B(Λ0) over the quantum affine algebra Uq(Cn(1)). In this paper, we construct the highest weight crystal B(Λ0) over the quantum affine algebra Uq(Cn(1)) using zigzag strip bundles, which completes the realizations of all highest weight crystals over Uq(g).",

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AB - Zigzag strip bundles are new 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). Recently, these models were used to the realization of highest weight crystals except for the highest weight crystal B(Λ0) over the quantum affine algebra Uq(Cn(1)). In this paper, we construct the highest weight crystal B(Λ0) over the quantum affine algebra Uq(Cn(1)) using zigzag strip bundles, which completes the realizations of all highest weight crystals over Uq(g).

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KW - Kashiwara embeddings

KW - Nakajima monomials

KW - Zigzag strip bundles

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Zigzag Strip Bundle Realization of B(Λ₀) over Uq(Cn(1))

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