Hurwitz Equivalence of Reflection Factorizations in Types B and D
Patrick Wegener
Abstract
A conjecture of Lewis asserts that two reflection factorizations of the same element in a finite Coxeter group W belong to the same Hurwitz orbit if and only if they generate the same subgroup H of W and have the same multiset of H-conjugacy classes. We prove this conjecture for every finite Coxeter group all of whose irreducible components are of type A, B or D. Furthermore we prove a reduction, which reduces the conjecture to a finite problem for the exceptional types.
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