标题： 抛物子群的正规化子与Artin-Tits群及Tits锥的交集 显示英文标题

标题： Normalisers of parabolic subgroups of Artin--Tits groups and Tits cone intersections

摘要： 设 $\Gamma$ 为一个考克斯特图，并让 $J \subseteq \Gamma$。 受3重翻转的启发，Iyama和Wemyss研究了 Tits锥中 $J$的交集中的超平面排列，这是经典考克斯特排列的 $J$-相对推广。 对于有限类型的 $\Gamma$，我们证明其复化超平面补集是与附属于 $J$的Artin-Tits群的标准抛物子群的正规izer（商）的 $K(\pi,1)$空间。 对于一般的$\Gamma$，我们证明了 Brink--Howlett 的范畴，该范畴描述了 Coxeter 群的抛物子群的正规化子，其万有覆盖由 Tits 锥交集的墙与房间结构所描述。我们利用这一点来证明墙交叉序列满足一个“原子 Matsumoto 关系”，推广了 Ko 的定理，并回答了 Iyama 和 Wemyss 提出的问题。 显示英文摘要

摘要： Let $\Gamma$ be a Coxeter diagram and let $J \subseteq \Gamma$. Motivated by 3-fold flops, Iyama and Wemyss study the hyperplane arrangement in the Tits cone intersection of $J$, which is a $J$-relative generalisation of the classical Coxeter arrangement. For $\Gamma$ of finite-type, we show that its complexified hyperplane complement is a $K(\pi,1)$ space for the normaliser (quotient) of the standard parabolic subgroup of the Artin--Tits group attached to $J$. For general $\Gamma$ we show that Brink--Howlett's groupoid, which describes normalisers of parabolic subgroups of Coxeter groups, has its universal cover described by the wall-and-chamber structure of the Tits cone intersection. We use this to show that wall crossing sequences satisfy an "atomic Matsumoto relation", generalising a theorem of Ko and answering questions raised by Iyama and Wemyss.