2023/12/27 by Hankyung Ko, Ko, Hankyung · 1 citation
Chemistry · #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #History and advancements in chemistry #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2312.16666
openalex publication_date 2023/12/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study parabolic double cosets in a Coxeter system by decomposing them into atom(ic coset)s, a generalization of simple reflections introduced in a joint work with Elias, Libedinsky, Patimo. We define and classify braid relations between compositions of atoms and prove a Matsumoto theorem. Together with a quadratic relation, our braid relations give a presentation of nilCoxeter algebroids similar to Demazure's presentation of nilCoxeter algebras. Our consideration of reduced compositions of atoms gives rise to a new combinatorial structure, which is equipped with a length function and a Bruhat order and is realized as Tits cone intersections in the sense of Iyama-Wemyss.