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Title: Representation Growth of Finitely Generated Torsion-Free Nilpotent Groups: Methods and Examples
Authors: Ezzat, Shannon
Keywords: torsion-free nilpotent groups
irreducible representations
zeta function
Issue Date: 2012
Abstract: This thesis concerns representation growth of finitely generated torsion-free nilpotent groups. This involves counting equivalence classes of irreducible representations and embedding this counting into a zeta function. We call this the representation zeta function. We use a new, constructive method to calculate the representation zeta functions of two families of groups, namely the Heisenberg group over rings of quadratic integers and the maximal class groups. The advantage of this method is that it is able to be used to calculate the p-local representation zeta function for all primes p. The other commonly used method, known as the Kirillov orbit method, is unable to be applied to these exceptional cases. Specifically, we calculate some exceptional p-local representation zeta functions of the maximal class groups for some well behaved exceptional primes. Also, we describe the Kirillov orbit method and use it to calculate various examples of p-local representation zeta functions for almost all primes p.
Publisher: University of Canterbury. Mathematics and Statistics
Degree: Doctor of Philosophy
URI: http://hdl.handle.net/10092/7235
Rights: Copyright Shannon Ezzat
Rights URI: http://library.canterbury.ac.nz/thesis/etheses_copyright.shtml
Appears in Collections:Engineering: Theses and Dissertations

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