论文标题
固定在将链球划分的绞线动作嵌入到匹配中的绞线动作中
An embedding of the skein action on set partitions into the skein action on matchings
论文作者
论文摘要
Rhoades定义了对称组对非交叉套件分区的绞线作用，该动作概括了对称组对匹配的作用。 $ \ mathfrak {s} _n $ - 通过托勒密关系使比赛成为可能，而设定分区上的操作是根据一组倾斜关系来定义的，该关系将ptolemy关系推广。对非交叉套件分区的链球作用已将应用于共变体理论和部分旗品种的环。在本文中，我们将展示如何将Rhoades的$ \ Mathfrak {s} _n $ - 模块嵌入到$ \ mathfrak {s} _n $模块中，从而产生了匹配，从而解释了Rhoades的广义链球关系。
Rhoades defined a skein action of the symmetric group on noncrossing set partitions which generalized an action of the symmetric group on matchings. The $\mathfrak{S}_n$-action on matchings is made possible via the Ptolemy relation, while the action on set partitions is defined in terms of a set of skein relations that generalize the Ptolemy relation. The skein action on noncrossing set partitions has seen applications to coinvariant theory and coordinate rings of partial flag varieties. In this paper, we will show how Rhoades' $\mathfrak{S}_n$-module can be embedded into the $\mathfrak{S}_n$-module generated by matchings, thereby explaining how Rhoades' generalized skein relations all arise from the Ptolemy relation.
