Crystal B(λ) as a subset of crystal B(∞) expressed as tableaux for An, type

JOURNAL OF ALGEBRA

卷:400

Article

Lee, Hyeonmi^1,2 

[1] Hanyang Univ, Dept Math, Seoul 133, South Korea

[2] Hanyang Univ, Res Inst Nat Sci, Seoul 133, South Korea

关键词: Crystal base;    Quantum group;    Special linear Lie algebra;    Marginally large tableau;    Marginally large reverse tableau;    Nakajima monomial;   

DOI  :  10.1016/j.jalgebra.2013.10.031

来源: Elsevier

【 摘 要 】

The crystal B (infinity) circle times T-lambda is known to contain a copy of the irreducible highest weight crystal B(lambda) as a sub-crystal. By explicitly identifying the elements belonging to the mentioned sub-crystal, we present two realizations of B(lambda) that are based on two realizations of B(infinity), for the special linear Lie algebra type. The first description of B(A) is based on our new realization of B(infinity) as the set of all marginally large reverse tableaux and the second is based on a previous realization of B(infinity) as the set of all marginally large tableaux. We further present two new Nakajima monomial realizations of B(lambda) that correspond naturally to our reverse. tableau and tableau realizations. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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