Bruhat intervals and parabolic cosets in arbitrary Coxeter groups
Combinatorics
2022-05-17 v1
Abstract
In [Journal of Pure and Applied Algebra {224} (2020), no 12, 106449], V. Mazorchuk and R. Mr{\dj}en (with some help by A. Hultman) prove that, given a Weyl group, the intersection of a Bruhat interval with a parabolic coset has a unique maximal element and a unique minimal element. We show that such intersections are actually Bruhat intervals also in the case of an arbitrary Coxeter group.
Keywords
Cite
@article{arxiv.2205.07733,
title = {Bruhat intervals and parabolic cosets in arbitrary Coxeter groups},
author = {Mario Marietti},
journal= {arXiv preprint arXiv:2205.07733},
year = {2022}
}