9 problems

Let $W$ be a well-generated finite complex reflection group, and let $T$ and $T'$ be reflection factorizations of a Coxeter element of $W$. Two factorizations are said to have the…

In either of the two settings, let $B$ be the associated braid group, let $W$ be the corresponding Coxeter or complex reflection group, let $p:B\twoheadrightarrow W$ be the natural…

Let $G$ be a complex reflection group and let $g\in G$. For a minimum-length reflection factorization $f$ of $g$, write $G_f$ for the subgroup generated by its factors, and conside…

Permutation-invariance conjecture. These two factorizations have Hurwitz orbits of equal size. The conjecture proposes that, in $G_6$, Hurwitz orbit size is unchanged by arbitraril…

Fix simple reflections $s_0,s_1,\ldots,s_{kn-1}$ in the hyperoctahedral group of type $B_{kn}$, with $(s_0s_1)^4=1$, and let $\mathbf{t}$ be the grouped factorization … The Hurwitz…

Let $c$ be a Coxeter element in G4, and let $T_1$ and $T_2$ be length-$m$ reflection factorizations of $c$. Suppose their multisets of conjugacy-class values are \\{1^a,2^b\} and…

Let $W$ be a reflection group whose generators all have order three. Let $c\in W$ be a Coxeter element. Let $T$ be a longer reflection factorization of $c$. The Hurwitz transitivit…

Let $W$ be a reflection group whose generators all have order three, let $c\in W$ be a Coxeter element, and let $T$ be a longer reflection factorization of $c$. A consecutive…

Let $c$ be a Singer cycle in $GL_n({\mathbb{F}}_q)$, and consider ordered factorizations $c=t_1t_2\cdots t_\ell$ into reflections. The multiset $\{\det(t_i)\}_{i=1}^\ell$ is an inv…