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.
| Identifer | oai:union.ndltd.org:canterbury.ac.nz/oai:ir.canterbury.ac.nz:10092/7235 |
| Date | January 2012 |
| Creators | Ezzat, Shannon |
| Publisher | University of Canterbury. Mathematics and Statistics |
| Source Sets | University of Canterbury |
| Language | English |
| Detected Language | English |
| Type | Electronic thesis or dissertation, Text |
| Rights | Copyright Shannon Ezzat, http://library.canterbury.ac.nz/thesis/etheses_copyright.shtml |
| Relation | NZCU |
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