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Non‐Monomial Unitary Representations of Nilpotent Groups I: The Abelian Case
Author(s) -
Carey A. L.,
Moran W.
Publication year - 1983
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-46.1.53
Subject(s) - mathematics , nilpotent , abelian group , monomial , unitary state , pure mathematics , nilpotent group , algebra over a field , combinatorics , political science , law
Let G be a discrete abelian group on which there is a multiplier σ: G × G → T. It is shown that if all the irreducible representations of ( G ,σ) are induced from 1‐dimensional representations of subgroups then all of the representations of ( G ,σ) are Type I. This represents the first step in the proof of the corresponding result for arbitrary discrete nilpotent groups.