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Mat. Zametki, 2007, Volume 82, Issue 3, Pages 383–389 (Mi mz3841)  

Nonstandard Representations of Locally Compact Groups

V. A. Lyubetskii, S. A. Pirogov

Institute for Information Transmission Problems, Russian Academy of Sciences

Abstract: In the note, it is proved that, under natural conditions, any infinite-dimensional unitary representation $T$ of a direct product of groups $G=K\times N$, where $K$ is a compact group and $N$ is a locally compact Abelian group, is imaged by a representation of the nonstandard analog $\widetilde G$ of the group $G$ in the group of nonstandard matrices of a fixed nonstandard size.

Keywords: unitary representation, nonstandard matrix, imaging of groups, Boolean algebra, Stone space, Casimir operator

DOI: https://doi.org/10.4213/mzm3841

Full text: PDF file (474 kB)
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English version:
Mathematical Notes, 2007, 82:3, 341–346

Bibliographic databases:

UDC: 510.225
Received: 29.11.2005
Revised: 29.01.2007

Citation: V. A. Lyubetskii, S. A. Pirogov, “Nonstandard Representations of Locally Compact Groups”, Mat. Zametki, 82:3 (2007), 383–389; Math. Notes, 82:3 (2007), 341–346

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