Rationality of twist representation zeta functions of compact $p$-adic analytic groups

Autor:	Stasinski, Alexander, Zordan, Michele
Rok vydání:	2022
Předmět:	Mathematics - Group Theory Primary 20E18 Secondary 20C15 22E35 20J06
Druh dokumentu:	Working Paper
Popis:	We prove that for any twist rigid compact $p$-adic analytic group $G$, its twist representation zeta function is a finite sum of terms $n_{i}^{-s}f_{i}(p^{-s})$, where $n_{i}$ are natural numbers and $f_{i}(t)\in\mathbb{Q}(t)$ are rational functions. Meromorphic continuation and rationality of the abscissa of the zeta function follow as corollaries. If $G$ is moreover a pro-$p$ group, we prove that its twist representation zeta function is rational in $p^{-s}$. To establish these results we develop a Clifford theory for twist isoclasses of representations, including a new cohomological invariant of a twist isoclass. Second part of arXiv:2007.10694. Comment: Author's Accepted Manuscript version. To appear in Trans. Amer. Math. Soc. Second part of arXiv:2007.10694
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2212.05825 Zobrazit plný text záznamu View this record from Arxiv