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

Stasinski, Alexander; Zordan, Michele

Abstract

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 −s i f i (p −s), where n i are natural numbers and f i (t) ∈ Q(t) are rational functions. Mero-morphic continuation and rationality of the abscissa of the zeta function follow as corollaries. If G is moreover a prop 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 coho-mological invariant of a twist isoclass.

Citation

Stasinski, A., & Zordan, M. (2024). Rationality of twist representation zeta functions of compact p-adic analytic groups. Transactions of the American Mathematical Society, 377, 7601-7631

• Journal Article Type: Article
• Acceptance Date: Apr 8, 2024
• Online Publication Date: Aug 30, 2024
• Publication Date: 2024-09
• Deposit Date: May 7, 2024
• Publicly Available Date: Oct 17, 2024
• Journal: Transactions of the American Mathematical Society
• Print ISSN: 0002-9947
• Electronic ISSN: 1088-6850
• Publisher: American Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 377
• Pages: 7601-7631
• Public URL: https://durham-repository.worktribe.com/output/2433997