Representation zeta functions of some nilpotent groups associated to prehomogeneous vector spaces
-
Alexander Stasinski
and
Christopher Voll
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
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
Funding statement: 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.
Acknowledgements
The remarks of two anonymous referees helped to improve this paper’s exposition.
References
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© 2017 by De Gruyter
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- Frontmatter
- Probabilistic trace and Poisson summation formulae on locally compact abelian groups
- The Selberg trace formula as a Dirichlet series
- On the cohomology and their torsion of real toric objects
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- Non-abelian tensor and exterior products of multiplicative Lie rings
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- On subordinate random walks
- Tame combings and easy groups
- On Belk’s classifying space for Thompson’s group F
- Subspace confinement for switched linear systems
- Exceptional bundles of homological dimension ${k}$
- Representation zeta functions of some nilpotent groups associated to prehomogeneous vector spaces
- Bockstein homomorphisms for Hochschild cohomology of group algebras and of block algebras of finite groups
Articles in the same Issue
- Frontmatter
- Probabilistic trace and Poisson summation formulae on locally compact abelian groups
- The Selberg trace formula as a Dirichlet series
- On the cohomology and their torsion of real toric objects
- Outer automorphism groups of simple Lie algebras and symmetries of painted diagrams
- Non-abelian tensor and exterior products of multiplicative Lie rings
- On the infimum of the spectrum of a relativistic Schrödinger operator
- Character correspondences for symmetric groups and wreath products
- Univalence in locally cartesian closed ∞-categories
- On subordinate random walks
- Tame combings and easy groups
- On Belk’s classifying space for Thompson’s group F
- Subspace confinement for switched linear systems
- Exceptional bundles of homological dimension ${k}$
- Representation zeta functions of some nilpotent groups associated to prehomogeneous vector spaces
- Bockstein homomorphisms for Hochschild cohomology of group algebras and of block algebras of finite groups
