Absolute order and involutions

Abstract

We study the restriction of the absolute order on a Coxeter group $W$ to an interval $[1,w{]}_T$, where $w\in W$ is an involution. We characterize and classify those involutions $w$ for which $[1,w{]}_T$ is a lattice, using the notion of involutive parabolic subgroups.

9 pages, 1 figure. Comments welcome!