The crossing model for regular An-crystals

JOURNAL OF ALGEBRA

卷:320

Article

Danilov, Vladimir I.²  Karzanov, Alexander V.¹  Koshevoy, Gleb A.² 

[1] Russian Acad Sci, Inst Syst Anal, Moscow 117312, Russia

[2] Russian Acad Sci, Cent Inst Econ & Math, Moscow 117418, Russia

关键词: Simply-laced algebra;    Crystal of representation;    Gelfand-Tsetlin pattern;   

DOI  :  10.1016/j.jalgebra.2008.08.006

来源: Elsevier

【 摘 要 】

A regular A(n)-crystal is an edge-colored directed graph, with n colors, related to an irreducible highest weight integrable module over U-q(sl(n+1)). Based on Stembridge's local axioms for regular simply-laced crystals and a structural characterization of regular A(2)-crystals in [V.I. Danilov, AN. Karzanov, G.A. Koshevoy, Combinatorics of regular A(2)-crystals, J. Algebra 310 (2007) 218-234], we present a new combinatorial construction, the so-called crossing model, and prove that this model generates precisely the set of regular A(n)-crystals. Using the model, we obtain a series of results on the combinatorial structure of such crystals and properties of their subcrystals. (C) 2008 Elsevier Inc. All rights reserved.

【 授权许可】

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