The parabolic coset structure of Bruhat intervals in Coxeter groups
Combinatorics
2022-05-24 v2
Abstract
In this paper, we study the decomposition of Bruhat intervals in a Coxeter group with respect to cosets of a parabolic subgroup. Our main result is that the intersection of a lower Bruhat interval with a parabolic coset contains a unique maximal element. As an application, we give a decomposition formula for the Poincar\'{e} polynomial of a Coxeter group element. We also show that the fibers of standard parabolic projection maps on Schubert varieties are themselves Schubert varieties.
Keywords
Cite
@article{arxiv.2204.11959,
title = {The parabolic coset structure of Bruhat intervals in Coxeter groups},
author = {Suho Oh and Edward Richmond},
journal= {arXiv preprint arXiv:2204.11959},
year = {2022}
}
Comments
11 pages, 2 figures. Ver2: Updated Section 2 with more background. Updated example at the end of Section 3