Modified Nakajima monomials and the crystal B (∞)

Seok Jin Kang; Jeong Ah Kim; Dong Uy Shin

doi:10.1016/j.jalgebra.2006.09.022

Modified Nakajima monomials and the crystal B (∞)

Seok Jin Kang, Jeong Ah Kim, Dong Uy Shin

Department of Mathematics

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

21 Scopus citations

Abstract

In this paper, we give a new realization of the crystal B (∞) using modified Nakajima monomials. For the quantum affine algebras of type A_n⁽¹⁾, we give an explicit characterization of the monomials in B (∞), and construct a natural crystal isomorphism between monomial realization and path realization. As a corollary, we obtain a new realization of the crystal B (∞) for the quantum classical algebras of type A_n.

Original language	English
Pages (from-to)	524-535
Number of pages	12
Journal	Journal of Algebra
Volume	308
Issue number	2
DOIs	https://doi.org/10.1016/j.jalgebra.2006.09.022
State	Published - 15 Feb 2007

Keywords

Crystal bases
Modified Nakajima monomials

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10.1016/j.jalgebra.2006.09.022

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title = "Modified Nakajima monomials and the crystal B (∞)",

abstract = "In this paper, we give a new realization of the crystal B (∞) using modified Nakajima monomials. For the quantum affine algebras of type An(1), we give an explicit characterization of the monomials in B (∞), and construct a natural crystal isomorphism between monomial realization and path realization. As a corollary, we obtain a new realization of the crystal B (∞) for the quantum classical algebras of type An.",

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AU - Kang, Seok Jin

AU - Kim, Jeong Ah

AU - Shin, Dong Uy

PY - 2007/2/15

Y1 - 2007/2/15

N2 - In this paper, we give a new realization of the crystal B (∞) using modified Nakajima monomials. For the quantum affine algebras of type An(1), we give an explicit characterization of the monomials in B (∞), and construct a natural crystal isomorphism between monomial realization and path realization. As a corollary, we obtain a new realization of the crystal B (∞) for the quantum classical algebras of type An.

AB - In this paper, we give a new realization of the crystal B (∞) using modified Nakajima monomials. For the quantum affine algebras of type An(1), we give an explicit characterization of the monomials in B (∞), and construct a natural crystal isomorphism between monomial realization and path realization. As a corollary, we obtain a new realization of the crystal B (∞) for the quantum classical algebras of type An.

KW - Crystal bases

KW - Modified Nakajima monomials

UR - https://www.scopus.com/pages/publications/33751424658

U2 - 10.1016/j.jalgebra.2006.09.022

DO - 10.1016/j.jalgebra.2006.09.022

M3 - Article

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SN - 0021-8693

VL - 308

SP - 524

EP - 535

JO - Journal of Algebra

JF - Journal of Algebra

IS - 2

ER -

Modified Nakajima monomials and the crystal B (∞)

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Keywords

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