Locally finite continuations and Coxeter groups of infinite ranks

Bernhard Mühlherr, Koji Nuida

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An involution r in a Coxeter group W is called an intrinsic reflection of W if r∈SW for each Coxeter generating set S of W. In recent joint work with R.B. Howlett [13] we determined all intrinsic reflections in finitely generated Coxeter groups. In the present paper we extend this result to the infinite rank case. An important tool in [13] is the notion of the finite continuation of an involution that is only meaningful for finitely generated Coxeter groups. Here we introduce the locally finite continuation for any subset of an arbitrary group which enables us to deal with Coxeter groups of infinite rank. We apply our result to show that certain classes of Coxeter groups are reflection independent and we investigate rigidity of 2-spherical Coxeter systems of arbitrary ranks.

Original languageEnglish
Article number106464
JournalJournal of Pure and Applied Algebra
Issue number1
Publication statusPublished - Jan 2021
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory


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