Geodesic
Nonstandard Representations of Locally Compact Groups
Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 383-389.

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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. 
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V. A. Lyubetskii; S. A. Pirogov. Nonstandard Representations of Locally Compact Groups. Matematičeskie zametki, Tome 82 (2007) no. 3, pp. 383-389. http://geodesic.mathdoc.fr/item/MZM_2007_82_3_a5/

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