This analysis classifies involutions in Coxeter groups, indicating when specific intervals form a lattice.
We study the restriction of the absolute order on a Coxeter group W to an interval [1,w]T, where w∈ 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.
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Thomas Gobet (2025) studied this question.
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