Nathan Chapelier‐Laget

collaborators

2 papers

math.RT2023

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

Nathan Chapelier-Laget, Thomas Gobet

We study the restriction of the strong Bruhat order on an arbitrary Coxeter group $W$ to cosets $x W_{L}^{θ}$ , where $x$ is an element of $W$ and $W_{L}^{θ}$ the subgroup of fixed points o…

math.CO2023

Low elements in dominant Shi regions

Nathan Chapelier-Laget

This note is a complement of a recent paper about low elements in affine Coxeter groups. We explain in terms of ad-nilpotent ideals of a Borel subalgebra why the minimal elements o…