Counting Irreducible Representations of the Discrete Heisenberg Group Over the Integers of a quadratic number field

Abstract

We calculate the representation growth zeta function of the discrete Heisenberg group over the integers of a quadratic number field. This is done by forming equivalence classes of representations, called twist iso-classes, and explicitly constructing a representative from each twist iso-class. Our method of construction involves studying the eigenspace structure of the elements of the image of the representation and then picking a suitable basis for the representation.

18 pages

References in corpus (2)

• Representation zeta functions of compact p-adic analytic groups and arithmetic groups
• Definable equivalence relations and zeta functions of groups

Cited by in corpus (1)

• Representation zeta functions of nilpotent groups and generating functions for Weyl groups of type B