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October 19, 20250 citationsOpen Access

Absolute order and involutions

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TGThomas Gobet

Key Points

  • Intervals defined by involutions exhibit lattice properties under certain conditions, highlighting structural complexity.
  • The study identifies specific involutions in Coxeter groups whose restricted absolute order forms a lattice, a crucial classification.
  • Characterizing the relationship between involutions and their corresponding parabolic subgroups underscores their role in lattice formation.
  • Using the notion of involutive parabolic subgroups, the study distinguishes when the intervals retain lattice structure.

Abstract

We study the restriction of the absolute order on a Coxeter group W to an interval 1, wT, where w W is an involution. We characterize and classify those involutions w for which 1, wT is a lattice, using the notion of involutive parabolic subgroups.

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Cite This Study

Thomas Gobet (2025) studied this question.

synapsesocial.com/papers/68f4b10d3d9d770bbc696df9https://doi.org/10.48550/arxiv.2507.11340
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