Subexpressions and the Bruhat order for double cosets
Combinatorics
2024-01-08 v2 Representation Theory
Abstract
The Bruhat order on a Coxeter group is often described by examining subexpressions of a reduced expression. We prove that an analogous description applies to the Bruhat order on double cosets. This establishes the compatibility of the Bruhat order on double cosets with concatenation, leading to compatibility between the monoidal structure and the ideal of lower terms in the singular Hecke 2-category. We also prove other fundamental properties of this ideal of lower terms.
Cite
@article{arxiv.2307.15726,
title = {Subexpressions and the Bruhat order for double cosets},
author = {Ben Elias and Hankyung Ko and Nicolas Libedinsky and Leonardo Patimo},
journal= {arXiv preprint arXiv:2307.15726},
year = {2024}
}
Comments
V2: Added a few new minor helpful results about the Bruhat order. Added a major portion of the paper which proves that the ideal of lower terms can be studied in several ways. Changed the introduction accordingly