A word property for twisted involutions in Coxeter groups

2017/04/26 by Hansson, Mikael, Hultman, Axel · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1704.08329

Abstract

Given an involutive automorphism θ of a Coxeter system (W,S), let \mathfrakI(θ) ⊆ 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 \underlineS-expressions (also known as admissible sequences, reduced I_θ-expressions, or involution words) for any given w ∈ \mathfrakI(θ). 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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