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

2010/05/17 by Shannon Ezzat, Ezzat, Shannon
Mathematics · #20C99 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:20C99

paper · pdf · doi:10.48550/arxiv.1005.2800

18 pages

arxiv created 2013/01/17 · arxiv updated 2013/01/18

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.

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