Representations of the discrete Heisenberg group and cocycles of an irrational rotation
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.
representations of the discrete Heisenberg group
scientific article; zbMATH DE number 4008700