Elements of minimal length and Bruhat order on fixed point cosets of Coxeter groups - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Elements of minimal length and Bruhat order on fixed point cosets of Coxeter groups

Résumé

We study the restriction of the strong Bruhat order on an arbitrary Coxeter group $W$ to cosets $x W_L^\theta$, where $x$ is an element of $W$ and $W_L^\theta$ the subgroup of fixed points of an automorphism $\theta$ of order at most two of a standard parabolic subgroup $W_L$ of $W$. When $\theta\neq\mathrm{id}$, there is in general more than one element of minimal length in a given coset, and we explain how to relate elements of minimal length. We also show that elements of minimal length in cosets are exactly those elements which are minimal for the restriction of the Bruhat order.

Dates et versions

hal-04322456 , version 1 (04-12-2023)

Identifiants

Citer

Nathan Chapelier-Laget, Thomas Gobet. Elements of minimal length and Bruhat order on fixed point cosets of Coxeter groups. 2023. ⟨hal-04322456⟩
28 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Mastodon Facebook X LinkedIn More