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Torsion pairs for quivers and the Weyl groups
Selecta Mathematica ( IF 1.4 ) Pub Date : 2020-06-29 , DOI: 10.1007/s00029-020-00563-9
Yuya Mizuno , Hugh Thomas

We give an interpretation of the map \(\pi ^c\) defined by Reading, which is a map from the elements of a Coxeter group to the c-sortable elements, in terms of the representation theory of preprojective algebras. Moreover, we study a close relationship between c-sortable elements and torsion pairs, and give an explicit description of the cofinite torsion classes in the context of the Coxeter group. As a consequence, we give a proof of some conjectures proposed by Oppermann, Reiten, and the second author.

中文翻译:

颤动和Weyl组的扭力对

我们根据预投影代数的表示理论,对由Reading定义的映射\(\ pi ^ c \)进行解释,该映射是从Coxeter组元素到c可排序元素的映射。此外,我们研究了c可排序元素与扭转对之间的紧密关系,并在Coxeter组的背景下给出了对有限扭转类的明确描述。因此,我们证明了Oppermann,Reiten和第二作者提出的一些猜想。
更新日期:2020-06-29
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