An explicit bijection between semistandard tableaux and non-elliptic sl3 webs
An explicit bijection between semistandard tableaux and non-elliptic sl3 webs
复制标题
半标准画面和非椭圆 sl3 网之间的显式双射
DOI：
10.1007/s10801-013-0428-y
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发表时间：
2012
影响因子：
0.8
通讯作者：
Heather M. Russell
中科院分区：
文献类型：
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作者：
Heather M. Russell
sl 3蜘蛛是一个用来研究量子群Uq（sl 3）的表示理论的图解范畴。这一范畴中的态射由非椭圆网的基生成。Khovanov-Kuperberg观察到，非椭圆形网是由半标准的杨氏图索引的。他们通过递归增长算法建立这种双射。最近，Tymoczko给出了一个简单的版本，这种双射的情况下，tableaux是标准的，并用它来研究旋转和加入的网页。本文基于Tymoczko的双射给出了构造所有非椭圆sl 3网的简单而明确的算法。作为一个应用程序，我们推广的结果Petersen-Pylyavskyy-Rhoades和Tymoczko证明，对于所有非椭圆的sl 3网站，旋转对应于jeu de taquin促进和加入对应于洗牌。
The sl3 spider is a diagrammatic category used to study the representation theory of the quantum group Uq(sl3). The morphisms in this category are generated by a basis of non-elliptic webs. Khovanov–Kuperberg observe that non-elliptic webs are indexed by semistandard Young tableaux. They establish this bijection via a recursive growth algorithm. Recently, Tymoczko gave a simple version of this bijection in the case that the tableaux are standard and used it to study rotation and join of webs. This article builds on Tymoczko’s bijection to give a simple and explicit algorithm for constructing all non-elliptic sl3 webs. As an application, we generalize results of Petersen–Pylyavskyy–Rhoades and Tymoczko proving that, for all non-elliptic sl3 webs, rotation corresponds to jeu de taquin promotion and join corresponds to shuffling.