Local Finiteness of the Twisted Bruhat Orders on Affine Weyl Groups
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 in J. Algebra, 163, 861--879 (1994). We also show that for a non-finite and non-cofinite biclosed set in the positive system of an affine root system with rank greater than 2, the set of elements having a fixed -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.
Keywords
Cite
@article{arxiv.1905.06580,
title = {Local Finiteness of the Twisted Bruhat Orders on Affine Weyl Groups},
author = {Weijia Wang},
journal= {arXiv preprint arXiv:1905.06580},
year = {2020}
}
Comments
v3: 23 pages, further expanded and a new section added