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Intrinsic reflections and strongly rigid Coxeter groups
Author(s) -
Howlett Robert B.,
Mühlherr Bernhard,
Nuida Koji
Publication year - 2018
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms.12090
Subject(s) - coxeter group , coxeter element , coxeter complex , mathematics , longest element of a coxeter group , conjugacy class , artin group , point group , combinatorics , pure mathematics
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 s ∈ S is conjugate to an element r ∈ R . 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.