1. CJM 2008 (vol 60 pp. 297)
|Transitive Factorizations in the Hyperoctahedral Group |
The classical Hurwitz enumeration problem has a presentation in terms of transitive factorizations in the symmetric group. This presentation suggests a generalization from type~$A$ to other finite reflection groups and, in particular, to type~$B$. We study this generalization both from a combinatorial and a geometric point of view, with the prospect of providing a means of understanding more of the structure of the moduli spaces of maps with an $\gS_2$-symmetry. The type~$A$ case has been well studied and connects Hurwitz numbers to the moduli space of curves. We conjecture an analogous setting for the type~$B$ case that is studied here.
Categories:05A15, 14H10, 58D29