Related papers: Hurwitz Actions on Reflection Factorizations in Co…

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…

We prove that the Hurwitz action on reflection factorizations of Coxeter elements is transitive up to certain natural constraints in the complex reflection groups G4 and G5. This affirms a more general conjecture by Lewis and Reiner in…

We prove that two reflection factorizations of a parabolic quasi-Coxeter element in a finite Coxeter group belong to the same Hurwitz orbit if and only if they generate the same subgroup and have the same multiset of conjugacy classes. As a…

We investigate the so-called dual Matsumoto property or Hurwitz action in finite, affine and arbitrary Coxeter groups. In particular, we want to investigate how to reduce reflection factorizations and how two reflection factorizations of…

In a finite real reflection group, two factorizations of a Coxeter element into an arbitrary number of reflections are shown to lie in the same orbit under the Hurwitz action if and only if they use the same multiset of conjugacy classes.…

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…

We show that the Hurwitz action is "as transitive as possible" on reflection factorizations of Coxeter elements in the well-generated complex reflection groups $G(d, 1, n)$ (the group of $d$-colored permutations) and $G(d, d, n)$.

We enumerate Hurwitz orbits of shortest reflection factorizations of an arbitrary element in the infinite family $G(m, p, n)$ of complex reflection groups. As a consequence, we characterize the elements for which the action is transitive…

We study the Hurwitz action of the classical braid group on factorisations of a Coxeter element c in a well-generated complex reflection group W. It is well-known that the Hurwitz action is transitive on the set of reduced decompositions of…

We provide a variety of cases in which two factorizations have Hurwitz orbits of the same size. We begin with prototypical results about factorizations of length two, and show that cycling elements or flipping and inverting elements in any…

We show that for a parabolic quasi-Coxeter element in an affine Coxeter group the Hurwitz action on its set of reduced factorizations into a product of reflections is transitive. We call an element of the Coxeter group parabolic…

Given an irreducible well-generated complex reflection group W with Coxeter number h, we call a Coxeter element any regular element (in the sense of Springer) of order h in W; this is a slight extension of the most common notion of Coxeter…

We give uniform formulas for the number of full reflection factorizations of a parabolic quasi-Coxeter element in a Weyl group or complex reflection group, generalizing the formula for the genus-0 Hurwitz numbers. This paper is the…

We define parabolic quasi-Coxeter elements in well generated complex reflection groups. We characterize them in multiple natural ways, and we study two combinatorial objects associated with them: the collections $\operatorname{Red}_W(g)$ of…

For well-generated complex reflection groups, Chapuy and Stump gave a simple product for a generating function counting reflection factorizations of a Coxeter element by their length. This is refined here to record the number of reflections…

The classical Hurwitz numbers count the fixed-length transitive transposition factorizations of a permutation, with a remarkable product formula for the case of minimum length (genus $0$). We study the analogue of these numbers for…

We enumerate factorizations of a Coxeter element in a well generated complex reflection group into arbitrary factors, keeping track of the fixed space dimension of each factor. In the infinite families of generalized permutations, our…

We provide a necessary and sufficient condition on an element of a finite Coxeter group to ensure the transitivity of the Hurwitz action on its set of reduced decompositions into products of reflections. We show that this action is…

For a finite real reflection group $W$ with Coxeter element $\gamma$ we give a uniform proof that the closed interval, $[I, \gamma]$ forms a lattice in the partial order on $W$ induced by reflection length. The proof involves the…

Orbits of the Weyl reflection groups attached to the simple Lie groups $A_2, C_2, G_2$ and Coxeter group $H_2$ are considered. For each of the groups products of any two orbits are decomposed into the union of the orbits. Results are…