Heisenberg subgroups of semisimple Lie groups

descriptionPublicationkeyboard_double_arrow_right Article 01 Aug 1975 English Publisher:AIP PublishingJournal:Journal of Mathematical Physics, volume 16, pages 1,646-1,648 (issn: 0022-2488, eissn: 1089-7658,

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Authors: Scull, Sidney C.;

doi: 10.1063/1.522720

Heisenberg subgroups of semisimple Lie groups

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Abstract

The restriction of a unitary representation of a semisimple Lie group to a Heisenberg subgroup Hn is shown to be quasiequivalent to the regular representation of Hn. Spectral properties of elements of the Heisenberg subgroup are described. Conditions under which an element of a semisimple Lie algebra may be embedded in a Heisenberg algebra are found.

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York University
Canada

Keywords

Applications of Lie groups to the sciences; explicit representations, Lie algebras of Lie groups

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