论文标题
反射组的Hurwitz编号II：抛物线式准氧气元素
Hurwitz numbers for reflection groups II: Parabolic quasi-Coxeter elements
论文作者
论文摘要
我们在复杂的复杂反射组中定义了抛物线准氧气元素。我们以多种自然方式表征它们，我们研究了两个与之相关的组合对象：收集$ \ operatotorname {red} _w（g）$减少了$ g $的反射因素化和$ \ operatatorName {rgs}（rgs}（rgs}（w，g）$ g $ g $ g $ g $的相对产生集。我们为抛物线式准氧气元素的大家族计算这些集合的基础性，尤其是我们将尺寸$ \＃\ propatatorName {red} _W（g）$与Frobenius歧管的几何不变剂相关联。本文在三个系列中排名第二。我们将依靠其在第三部分中的许多结果来证明统一的公式，这些公式列举了抛物线准氧气元素的完全反思因素化，从而推广了属-0 $ 0 $ hurwitz的数字。
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 reduced reflection factorizations of $g$ and $\operatorname{RGS}(W,g)$ of the relative generating sets of $g$. We compute the cardinalities of these sets for large families of parabolic quasi-Coxeter elements and, in particular, we relate the size $\#\operatorname{Red}_W(g)$ with geometric invariants of Frobenius manifolds. This paper is second in a series of three; we will rely on many of its results in part III to prove uniform formulas that enumerate full reflection factorizations of parabolic quasi-Coxeter elements, generalizing the genus-$0$ Hurwitz numbers.
