Representations of the discrete Heisenberg group and cocycles of an irrational rotation
type: Item
instance of: scholarly article
title: Representations of the discrete Heisenberg group and cocycles of an irrational rotation
zbMATH Open document ID: 0622.22007
author: Wesley E. Mitchell
author: Arlan Ramsay
author: Lawrence W. Baggett
published in: Michigan Mathematical Journal
publication date: 1984-01-01T00:00:00Z
review text: The main purpose of this paper is to present some information about (one- ) cocycles of irrational rotations in the context of representation theory, and to raise a few questions in that same context. The existence of irreducible cocycles of every dimension is known from general arguments and explicit formulas have been given in some cases. Our interest is in specific formulas, just as specific formulas are sought when studying group representations. Indeed, we derive cocycle formulas from formulas for representations of the discrete Heisenberg group, and then use the cocycles to get formulas for representations of the Mautner group. Thus we are closely tied to representation theory in our motivation and in our method. Besides the explicitness of the cocycle formulas, we want to emphasize that they arise in a systematic way in the representation theory setting.
Mathematics Subject Classification ID: 22D40
zbMATH DE Number: 4008700
zbMATH Keywords: cocycles of irrational rotations
zbMATH Keywords: cocycle formulas
zbMATH Keywords: representations of the discrete Heisenberg group
zbMATH Keywords: Mautner group
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029003072
OpenAlex ID: W2009184241
DOI: 10.1307/MMJ/1029003072
description: scientific article; zbMATH DE number 4008700