Zeta functions of groups - singular Pfaffians
Zeta functions of groups - singular Pfaffians
The local normal zeta functions of a finitely generated, torsion-free nilpotent group G of class 2 depend on the geometry of the Pfaffian hypersurface associated to the bilinear form induced by taking commutators in G.
The smallest examples of zeta functions which are not finitely uniform arise from groups whose associated Pfaffian hypersurfaces are plane curves. In this paper we study groups whose Pfaffians define singular curves, illustrating that the local normal zeta functions may indeed invoke all the degeneracy loci of the Pfaffian.
Zeta functions of groups, Bruhat-Tits buildings
Ramanujan Mathematical Society
Voll, Christopher
b7bd2890-38ac-4e05-adb7-3b376916ff79
Voll, Christopher
b7bd2890-38ac-4e05-adb7-3b376916ff79
Voll, Christopher
(2009)
Zeta functions of groups - singular Pfaffians.
In International Conference on Geometric Group Theory.
Ramanujan Mathematical Society.
15 pp
.
(In Press)
Record type:
Conference or Workshop Item
(Paper)
Abstract
The local normal zeta functions of a finitely generated, torsion-free nilpotent group G of class 2 depend on the geometry of the Pfaffian hypersurface associated to the bilinear form induced by taking commutators in G.
The smallest examples of zeta functions which are not finitely uniform arise from groups whose associated Pfaffian hypersurfaces are plane curves. In this paper we study groups whose Pfaffians define singular curves, illustrating that the local normal zeta functions may indeed invoke all the degeneracy loci of the Pfaffian.
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Accepted/In Press date: 13 November 2009
Venue - Dates:
International Conference on Geometric Group Theory, Assam, India, 2002-12-01 - 2002-12-01
Keywords:
Zeta functions of groups, Bruhat-Tits buildings
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Local EPrints ID: 69453
URI: http://eprints.soton.ac.uk/id/eprint/69453
PURE UUID: 2c1308fb-ddb2-4f9e-9dc3-0500e7806a01
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Date deposited: 13 Nov 2009
Last modified: 29 Jan 2020 13:01
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Contributors
Author:
Christopher Voll
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