Hurwitz equivalence of reflection factorizations in $G_7$

Colin Pirillo; Sarah Racile; Tyler Minnick; Yueqi Wang

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Hurwitz equivalence of reflection factorizations in $G_7$

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arxiv 2110.08371 v1 pith:7JXX7DLN submitted 2021-10-15 math.CO math.GR

Tyler Minnick , Colin Pirillo , Sarah Racile , Yueqi Wang This is my paper · ORCID

classification math.COmath.GR

keywords reflectionfactorizationssameclassescomplexconjugacyelementequivalence

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We prove that two reflection factorizations of a given element in an exceptional rank-2 complex reflection group of tetrahedral type are Hurwitz-equivalent if and only if they generate the same subgroup and have the same multiset of conjugacy classes.

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