Set Partitions, Fermions, and Skein Relations
Set Partitions, Fermions, and Skein Relations
复制标题
设置分区、费米子和绞纱关系
DOI：
10.1093/imrn/rnac110
复制
发表时间：
2022
影响因子：
1
通讯作者：
Rhoades, Brendon
中科院分区：
文献类型：
--
作者：
Kim, Jesse;Rhoades, Brendon
设和为两个变量列表，考虑的对角作用在由这些变量生成的外代数上。Jongwon Kim和第二作者定义并研究了由带消失常数项的-不变量生成的理想模化得到的费米子对角余不变环。另一方面，第二作者描述了一个行动的向量空间的基础上的非交叉集划分的使用一个新的家庭的绞关系，解决交叉集划分。我们给出了的一个自然Catalan维子模与skein表示之间的同构。要做到这一点，我们表明，集分区绞关系自然产生的外部代数的背景下。我们的方法产生一个等变的方式来解决交叉集分区。我们使用费米子澄清，锐化和扩展集分区交叉分辨率的理论。
Letandbe two lists ofvariables, and consider the diagonal action ofon the exterior algebragenerated by these variables. Jongwon Kim and the 2nd author defined and studied thefermionic diagonal coinvariant ringobtained fromby modding out by the ideal generated by the-invariants with vanishing constant term. On the other hand, the 2nd author described an action ofon the vector space with basis given by noncrossing set partitions ofusing a novel family of skein relations that resolve crossings in set partitions. We give an isomorphism between a natural Catalan-dimensional submodule ofand the skein representation. To do this, we show that set partition skein relations arise naturally in the context of exterior algebras. Our approach yields an-equivariant way to resolve crossings in set partitions. We use fermions to clarify, sharpen, and extend the theory of set partition crossing resolution.