Vanishing ranges for the mod $p$ cohomology of alternating subgroups of Coxeter groups

Toshiyuki Akita; Ye Liu

doi:10.1016/j.jalgebra.2016.11.005

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arXiv · 1604.08277

Vanishing ranges for the mod $p$ cohomology of alternating subgroups of Coxeter groups

Toshiyuki Akita·Ye Liu

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Abstract

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.

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BibTeX RIS

Toshiyuki Akita, Ye Liu. 2016-04-28. Vanishing ranges for the mod $p$ cohomology of alternating subgroups of Coxeter groups. https://doi.org/10.1016/j.jalgebra.2016.11.005

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