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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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Volume 29, Issue 3


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

Alexander Stasinski / Christopher Voll
Published Online: 2016-06-21 | DOI: https://doi.org/10.1515/forum-2015-0099


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.

Keywords: Finitely generated nilpotent groups; representation zeta functions; Igusa local zeta functions; prehomogeneous vector spaces

MSC 2010: 22E55; 20F69; 05A15; 11S90; 11M41


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About the article

Received: 2015-05-26

Revised: 2016-05-23

Published Online: 2016-06-21

Published in Print: 2017-05-01

Funding Source: Deutsche Forschungsgemeinschaft

Award identifier / Grant number: Sonderforschungsbereich 701 at Bielefeld University

Funding Source: Engineering and Physical Sciences Research Council

Award identifier / Grant number: EP/F044194/1

Voll acknowledges support by the DFG through Sonderforschungsbereich 701 at Bielefeld University and helpful conversations with Jan Schepers. This research was supported by Engineering and Physical Sciences Research Council grant EP/F044194/1.

Citation Information: Forum Mathematicum, Volume 29, Issue 3, Pages 717–734, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2015-0099.

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