论文标题
分类对称二重性的三个观点
Three perspectives on categorical symmetric Howe duality
论文作者
论文摘要
在本文中，我们考虑了Khovanov，Lauda，Sussan和Yonezawa引入的分类对称二元性。尽管最初是从纯图的角度定义的，但该结构也具有几何和表示理论解释，对应于箭袋代表空间上的某些不正正滑轮，以及$ \ mathfrak {gl} _n $的Gelfand-Tsetlin模块类别。 特别是，我们表明，在Khovanov-Lauda-Sussan-Yonezawa的工作中讨论的“韦伯斯特代数变形”表明了Gelfand-tsetlin模块类别之间的Koszul二重性，超过$ \ Mathfrak {gl} _n $，以及在构造的范围内，在lineal的代表下进行了某种代表，以下是一个偶然的代表。基地。此外，我们表明这种双重性与图形分类作用相结合。包括作者和Jerry Guan的附录。
In this paper, we consider the categorical symmetric Howe duality introduced by Khovanov, Lauda, Sussan and Yonezawa. While originally defined from a purely diagrammatic perspective, this construction also has geometric and representation-theoretic interpretations, corresponding to certain perverse sheaves on spaces of quiver representations and the category of Gelfand-Tsetlin modules over $\mathfrak{gl}_n$. In particular, we show that the "deformed Webster algebras" discussed in work of Khovanov-Lauda-Sussan-Yonezawa manifest a Koszul duality between blocks of the category of Gelfand-Tsetlin modules over $\mathfrak{gl}_n$, and the constructible sheaves on representations of a linear quiver invariant under a certain parabolic in the group that acts by changing bases. Furthermore, we show that this duality intertwines translation functors with a diagrammatic categorical action. Includes an appendix by the author and Jerry Guan.
