The intermediate orders of a Coxeter group
Combinatorics
2022-06-28 v2
Abstract
We define a class of partial orders on a Coxeter group associated with sets of reflections. In special cases, these lie between the left weak order and the Bruhat order. We prove that these posets are graded by the length function and that the projections on the right parabolic quotients are always order preserving. We also introduce the notion of -Bruhat graph, -absolute length and -absolute order, proposing some related conjectures and problems.
Cite
@article{arxiv.2203.00405,
title = {The intermediate orders of a Coxeter group},
author = {Angela Carnevale and Matthew Dyer and Paolo Sentinelli},
journal= {arXiv preprint arXiv:2203.00405},
year = {2022}
}
Comments
14 pages, to appear in Proc. Amer. Math. Soc