Intrinsic reflections in Coxeter systems
Abstract
Let (W,S) be a Coxeter system and let s ∈ S. We call s a right-angled generator of (W,S) if st = ts or st has infinite order for each t ∈ S. We call s an intrinsic reflection of W if s ∈ RW for all Coxeter generating sets R of W. We give necessary and sufficient conditions for a right-angled generator s ∈ S of (W,S) to be an intrinsic reflection of W.
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