Bruhat order and graph structures of lower intervals in Coxeter groups
Combinatorics
2018-12-18 v1
Abstract
We show that any lower Bruhat interval in a Coxeter group is a disjoint union of certain two-sided cosets as a consequence of Lifting Property and Subword Property. Furthermore, we describe these details in terms of Bruhat graphs, graded posets, and two-sided quotients altogether. For this purpose, we introduce some new ideas, quotient lower intervals and quotient Bruhat graphs.
Keywords
Cite
@article{arxiv.1812.06266,
title = {Bruhat order and graph structures of lower intervals in Coxeter groups},
author = {Masato Kobayashi},
journal= {arXiv preprint arXiv:1812.06266},
year = {2018}
}
Comments
18 pages