Intrinsic reflections and strongly rigid Coxeter groups:

Robert B. Howlett, Bernhard Mühlherr, Koji Nuida

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


It is possible for a group W that is abstractly isomorphic to a Coxeter group to have more than one conjugacy class of Coxeter generating sets, and if S and R are two non-conjugate Coxeter generating sets then it may or may not be the case that some element sϵS is conjugate to an element rϵR. In this paper we classify the so-called intrinsic reflections: those elements of W whose conjugacy class intersects non-trivially every Coxeter generating set. In combination with previously known results, this leads us to a classification of Coxeter groups for which all Coxeter generating sets are conjugate.

Original languageEnglish
Pages (from-to)534-574
Number of pages41
JournalProceedings of the London Mathematical Society
Issue number3
Publication statusPublished - Mar 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Mathematics


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