论文标题
反射亚组的辫子组
Braid groups of normalizers of reflection subgroups
论文作者
论文摘要
令$ W_0 $为有限复合体反射组$ W $的反射子组，让$ b_0 $和$ b $为他们各自的辫子组。为了构建Hecke Algebra $ \ widetilde {h} _0 $对于normanizer $ n_w（w_0）$，首先考虑一个天然的亚Quotient $ \ widetilde {b} _0 $ b $ $ b $，这是$ n_w（w_0）/w_0）的扩展名。我们证明，当$ W $是Coxeter组时，该扩展名是分开的，并推导Hecke代数$ \ widetilde {H} _0 $的标准基础。在非氧气情况下，我们还提供了拆分和非分类示例的类别。
Let $W_0$ be a reflection subgroup of a finite complex reflection group $W$, and let $B_0$ and $B$ be their respective braid groups. In order to construct a Hecke algebra $\widetilde{H}_0$ for the normalizer $N_W(W_0)$, one first considers a natural subquotient $\widetilde{B}_0$ of $B$ which is an extension of $N_W(W_0)/W_0$ by $B_0$. We prove that this extension is split when $W$ is a Coxeter group, and deduce a standard basis for the Hecke algebra $\widetilde{H}_0$. We also give classes of both split and non-split examples in the non-Coxeter case.
