当前位置: X-MOL 学术J. Group Theory › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Local finiteness of the twisted Bruhat orders on affine Weyl groups
Journal of Group Theory ( IF 0.5 ) Pub Date : 2020-08-19 , DOI: 10.1515/jgth-2020-0028
Weijia Wang 1
Affiliation  

Abstract In this paper, we investigate various properties of strong and weak twisted Bruhat orders on a Coxeter group. In particular, we prove that any twisted strong Bruhat order on an affine Weyl group is locally finite, strengthening a result of Dyer [Quotients of twisted Bruhat orders, J. Algebra 163 1994, 3, 861–879]. We also show that, for a non-finite and non-cofinite biclosed set B in the positive system of an affine root system with rank greater than 2, the set of elements having a fixed B-twisted length is infinite. This implies that the twisted strong and weak Bruhat orders have an infinite antichain in those cases. Finally, we show that twisted weak Bruhat order can be applied to the study of the tope poset of an infinite oriented matroid arising from an affine root system.

中文翻译:

仿射 Weyl 群上扭曲 Bruhat 阶数的局部有限性

摘要 在本文中,我们研究了 Coxeter 群上强弱扭曲 Bruhat 阶次的各种性质。特别是,我们证明了仿射 Weyl 群上的任何扭曲的强 Bruhat 阶次都是局部有限的,从而加强了 Dyer 的结果 [扭曲 Bruhat 阶数的商数,J. Algebra 163 1994, 3, 861–879]。我们还表明,对于秩大于 2 的仿射根系统的正系统中的非有限和非余有限双封闭集 B,具有固定 B 扭曲长度的元素集是无限的。这意味着在这些情况下,扭曲的强弱 Bruhat 阶数具有无限反链。最后,我们证明了扭曲弱 Bruhat 阶数可用于研究由仿射根系统产生的无限定向拟阵的顶偏序。
更新日期:2020-08-19
down
wechat
bug