Bender--Knuth Billiards in Coxeter Groups

Grant Barkley, Colin Defant, Eliot Hodges +2

Let $(W,S)$ be a Coxeter system, and write $S=\{s_i:i\in I\}$, where $I$ is a finite index set. Fix a nonempty convex subset $\mathcal{L}$ of $W$. If $W$ is of type $A$, then $\mat…