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

2015/05/26 by Alexander Stasinski, Stasinski, Alexander, Christopher Voll +1
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT

paper · pdf · doi:10.48550/arxiv.1505.06837

21 pages; minor changes of notation, fixed typos and clarifications

openalex publication_date 2015/05/26 · arxiv created 2016/05/24 · arxiv updated 2016/05/25 · openalex created_date 2022/08/19 · openalex updated_date 2026/07/28

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 \mathfrakp-adic integrals associated to certain rank varieties of matrices of linear forms.

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