Absolute order and involutions

preprint2025arXivOpen access

Abstract

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

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