Patrick Wegener, Sophiane Yahiatene
Abstract
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We extend a result of Lewis and Reiner from finite Coxeter groups to Coxeter groups of finite rank by showing that two reflection factorizations of a Coxeter element lie in the same Hurwitz orbit if and only if they share the same multiset of conjugacy classes.
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We extend a result of Lewis and Reiner from finite Coxeter groups to Coxeter groups of finite rank by showing that two reflection factorizations of a Coxeter element lie in the same Hurwitz orbit if and only if they share the same multiset of conjugacy classes.
Key concepts: Coxeter group, Coxeter element, Longest element of a Coxeter group, Point group, Coxeter complex, Conjugacy class, Mathematics, Artin group