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arXiv · 1704.08329

A word property for twisted involutions in Coxeter groups

Mikael Hansson·Axel Hultman
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Abstract

Given an involutive automorphism $\theta$ of a Coxeter system $(W,S)$, let $\mathfrak{I}(\theta) \subseteq W$ denote the set of twisted involutions. We provide a minimal set of moves that can be added to the braid moves, in order to connect all reduced $\underline{S}$-expressions (also known as admissible sequences, reduced $I_\theta$-expressions, or involution words) for any given $w \in \mathfrak{I}(\theta)$. This can be viewed as an analogue of the well-known word property for Coxeter groups. It improves upon a result of Hamaker, Marberg, and Pawlowski, and generalises similar statements valid in certain types due to Hu, Zhang, Wu, and Marberg.

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Mikael Hansson, Axel Hultman. 2017-04-26. A word property for twisted involutions in Coxeter groups. https://arxiv.org/abs/1704.08329

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