Representation zeta functions of some nilpotent groups associated to prehomogeneous vector spaces

Stasinski, Alexander; Voll, Christopher

Abstract

We compute the representation zeta functions of some finitely generated nilpotent groups associated to unipotent group schemes over rings of integers in number fields. These group schemes are defined by Lie lattices whose presentations are modelled on certain prehomogeneous vector spaces. Our method is based on evaluating p-adic integrals associated to certain rank varieties of matrices of linear forms.

Citation

Stasinski, A., & Voll, C. (2017). Representation zeta functions of some nilpotent groups associated to prehomogeneous vector spaces. Forum Mathematicum, 29(3), 717-734. https://doi.org/10.1515/forum-2015-0099

• Journal Article Type: Article
• Acceptance Date: May 23, 2016
• Online Publication Date: Jun 21, 2016
• Publication Date: May 1, 2017
• Deposit Date: Jul 14, 2016
• Publicly Available Date: Jun 21, 2017
• Journal: Forum Mathematicum
• Print ISSN: 0933-7741
• Electronic ISSN: 1435-5337
• Publisher: De Gruyter
• Peer Reviewed: Peer Reviewed
• Volume: 29
• Issue: 3
• Pages: 717-734
• DOI: https://doi.org/10.1515/forum-2015-0099
• Public URL: https://durham-repository.worktribe.com/output/1407762