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Bruhat inversions in Weyl groups and torsion-free classes over preprojective algebras
Communications in Algebra ( IF 0.6 ) Pub Date : 2021-01-17 , DOI: 10.1080/00927872.2020.1866592
Haruhisa Enomoto 1
Affiliation  

Abstract

For an element w of a simply-laced Weyl group, Buan-Iyama-Reiten-Scott defined a subcategory F(w) of the module category over the preprojective algebra of Dynkin type. This paper studies categorical properties of F(w) using the root system. We show that simple objects in F(w) bijectively correspond to Bruhat inversion roots of w, and obtain a combinatorial criterion for F(w) to satisfy the Jordan-Hölder property (JHP). For type A case, we give a diagrammatic construction of simple objects, and show that (JHP) can be characterized via a forest-like permutation, introduced by Bousquet-Mélou and Butler in the study of Schubert varieties.



中文翻译:

预投影代数上的Weyl群和无扭转类中的Bruhat反转

摘要

对于简单定位的Weyl组的元素w,Buan-Iyama-Reiten-Scott定义了一个子类别FwDynkin类型的预投影代数上的模数类别的集合。本文研究了分类的性质Fw使用根系统。我们展示了简单的对象Fw双射地对应于w的Bruhat反演根,并获得w的组合准则Fw满足约旦·霍尔德(JHP)的财产。对于A型案例,我们给出了简单对象的图解结构,并表明(JHP)可以通过类似森林的排列来表征,这是Bousquet-Mélou和Butler在研究Schubert品种时引入的。

更新日期:2021-03-21
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