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

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

2010-05-17

arxiv.org/abs/1005.2800v1

Mathematics

Group Theory

16 pages

Scientific paper

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.

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