Abstract
We extend a result of Lewis and Reiner from finite Coxeter groups to all Coxeter groups 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.
Highlights
Given a Coxeter system (W, S) with set of reflections T, the braid group acts on reflection factorizations of a given element w ∈ W, that is it acts on tuples (t1, . . . , tm) ∈ T m of reflections such that w = t1 · · · tm
For a definition) acts on reflection factorizations of a given element w ∈ W, that is it acts on tuples (t1, . . . , tm) ∈ T m of reflections such that w = t1 · · · tm
We call a reflection factorization (t1, . . . , tm) of an element w ∈ W reduced if w cannot be written as a product of less than m reflections
Summary
Given a Coxeter system (W, S) with set of reflections T , the braid group For a definition) acts on reflection factorizations of a given element w ∈ W , that is it acts on tuples Its inverse σi−1) acts by a Hurwitz move on a reflection factorization: σi(t1, .
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