标题： Springer 族对于良好生成的复数辫群中的正则中心化子 显示英文标题

标题： Springer categories for regular centralizers in well-generated complex braid groups

摘要： 在证明复反射排列的K(π,1)猜想中，Bessis定义了适合研究Springer正则元中心化子的辫群的Garside范畴。我们对这些范畴进行了详细研究，我们称之为Springer范畴。特别是，我们描述了正则中心化子中的辫式反射的共轭性，这是通过相关Springer范畴的Garside结构来表述的。通过这样做，我们得到了一个纯Garside理论证明，这是Digne、Marin和Michel关于有限指数子群在复辫群中的中心定理在正则中心化子情况下的一种证明。我们还提供了Springer范畴的“Hurwitz-like”表示。为此，我们对无限系列中的非交叉划分提供了额外的见解。最后，我们使用这种“Hurwitz-like”表示，以及我们为范畴引入的广义Reidemeister-Schreier方法，推导出复辫群B(G31)的良好表示。 显示英文摘要

摘要： In his proof of the K(pi,1) conjecture for complex reflection arrangements, Bessis defined Garside categories suitable for studying braid groups of centralizers of Springer regular elements in well-generated complex reflection groups. We provide a detailed study of these categories, which we call Springer categories. We describe in particular the conjugacy of braided reflections of regular centralizer in terms of the Garside structure of the associated Springer category. In so doing we obtain a pure Garside theoretic proof of a theorem of Digne, Marin and Michel on the center of finite index subgroups in complex braid groups in the case of a regular centralizer in a well-generated group. We also provide a "Hurwitz-like" presentation of Springer categories. To this aim we provide additional insights on noncrossing partitions in the infinite series. Lastly, we use this "Hurwitz-like" presentation, along with a generalized Reidemeister-Schreier method we introduce for groupoids, to deduce nice presentations of the complex braid group B(G31).