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ABSOLUTE ORDER AND INVOLUTIONS

Part of: Special aspects of infinite or finite groups

Published online by Cambridge University Press:  23 October 2025

THOMAS GOBET Open the ORCID record for THOMAS GOBET [Opens in a new window]
THOMAS GOBET*
Affiliation:
Université Clermont Auvergne , LMBP, UMR 6620 (CNRS), Campus des Cézeaux, 3 place Vasarely, TSA 60026, CS 60026, 63178 Aubière cedex, France
*
e-mail: thomas.gobet@uca.fr
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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 characterise and classify those involutions w for which $[1,w]_T$ is a lattice, using the notion of involutive parabolic subgroups.

Keywords

reflection groupsCoxeter groups

MSC classification

Primary: 20F55: Reflection and Coxeter groups

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 12
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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