无限秩仿射李代数上的极值权晶体

IF 0.5 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2024-12-21 DOI:10.1007/s10468-024-10302-9

Taehyeok Heo

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引用次数: 0

摘要

我们用组合模型解释了无限秩仿射李代数上的极值权晶体：由Kwon提出的旋量模型和由Lecouvey提出的无限秩模拟Kashiwara-Nakashima表。特别地，我们证明了Lecouvey的表模型与零级极值权晶体是同构的。利用这些组合模型，我们解释了一类由一些极重晶体组成的格罗滕迪克环的代数结构。

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Extremal Weight Crystals Over Affine Lie Algebras of Infinite Rank

We explain extremal weight crystals over affine Lie algebras of infinite rank using combinatorial models: a spinor model due to Kwon, and an infinite rank analogue of Kashiwara-Nakashima tableaux due to Lecouvey. In particular, we show that Lecouvey’s tableau model is isomorphic to an extremal weight crystal of level zero. Using these combinatorial models, we explain an algebra structure of the Grothendieck ring for a category consisting of some extremal weight crystals.

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来源期刊

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.