Generalized young walls and crystal bases for quantum affine algebra of type A

Jeong Ah Kim; Dong Uy Shin

doi:10.1090/S0002-9939-2010-10428-8

Generalized young walls and crystal bases for quantum affine algebra of type A

Jeong Ah Kim, Dong Uy Shin

Department of Mathematics

Hanyang University

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

8 Scopus citations

Abstract

We give a new realization of the crystal B(∞) of U^- _q (A⁽¹⁾_n) using generalized Young walls, a modified notion of Young walls of type A⁽¹⁾_n Moreover, by the fact that the irreducible highest weight crystal B(λ) lies in the crystal B(∞)⊗ Rλ, we construct the crystal B(λ) using generalized Young walls.

Original language	English
Pages (from-to)	3877-3889
Number of pages	13
Journal	Proceedings of the American Mathematical Society
Volume	138
Issue number	11
DOIs	https://doi.org/10.1090/S0002-9939-2010-10428-8
State	Published - Nov 2010

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title = "Generalized young walls and crystal bases for quantum affine algebra of type A",

abstract = "We give a new realization of the crystal B(∞) of U- q (A(1)n) using generalized Young walls, a modified notion of Young walls of type A(1)n Moreover, by the fact that the irreducible highest weight crystal B(λ) lies in the crystal B(∞)⊗ Rλ, we construct the crystal B(λ) using generalized Young walls.",

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AU - Shin, Dong Uy

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N2 - We give a new realization of the crystal B(∞) of U- q (A(1)n) using generalized Young walls, a modified notion of Young walls of type A(1)n Moreover, by the fact that the irreducible highest weight crystal B(λ) lies in the crystal B(∞)⊗ Rλ, we construct the crystal B(λ) using generalized Young walls.

AB - We give a new realization of the crystal B(∞) of U- q (A(1)n) using generalized Young walls, a modified notion of Young walls of type A(1)n Moreover, by the fact that the irreducible highest weight crystal B(λ) lies in the crystal B(∞)⊗ Rλ, we construct the crystal B(λ) using generalized Young walls.

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U2 - 10.1090/S0002-9939-2010-10428-8

DO - 10.1090/S0002-9939-2010-10428-8

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VL - 138

SP - 3877

EP - 3889

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

IS - 11

ER -

Generalized young walls and crystal bases for quantum affine algebra of type A

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