Article ID Journal Published Year Pages File Type
4585090 Journal of Algebra 2014 16 Pages PDF
Abstract

We calculate the representation zeta function of the Heisenberg group over the integers of a quadratic number field. In general, the representation zeta function of a finitely generated torsion-free nilpotent group enumerates equivalence classes of representations, called twist-isoclasses. This calculation is based on an explicit description of a representative from each twist-isoclass. 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 underlying vector space.

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Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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