Vanishing ranges for the mod p cohomology of alternating subgroups of Coxeter groups
Vanishing ranges for the mod p cohomology of alternating subgroups of Coxeter groups
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Coxeter 群交替子群的 mod p 上同调的消失范围
DOI：
10.1016/j.jalgebra.2016.11.005
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发表时间：
2017
影响因子：
0.9
通讯作者：
Ye
中科院分区：
文献类型：
--
作者：
Akita;Toshiyuki; Liu;Ye
我们获得有限 p 无 Coxeter 群的交替子群的 mod p 上同调的消失范围。这里，如果对于 W 的每对 Coxeter 生成器 s、t，乘积 st 的阶数与 p 互质，则 Coxeter 群 W 是 p-free。我们的结果概括了先前由 Kleshchev-Nakano 和 Burichenko 证明的交替群的结果。作为副产品，我们获得了有限 p 无 Coxeter 群的扭曲上同调的消失范围，其系数位于符号表示中。此外，针对某一类无限 Coxeter 群，证明了主要结果的弱版本。
We obtain vanishing ranges for the mod p cohomology of alternating subgroups of finite p-free Coxeter groups. Here a Coxeter group W is p-free if the order of the product st is prime to p for every pair of Coxeter generators s, t of W. Our result generalizes those for alternating groups formerly proved by Kleshchev–Nakano and Burichenko. As a byproduct, we obtain vanishing ranges for the twisted cohomology of finite p-free Coxeter groups with coefficients in the sign representations. In addition, a weak version of the main result is proved for a certain class of infinite Coxeter groups.