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Canonical Representations on Lobachevsky Spaces: An Interaction with an Overalgebra

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Abstract

We define canonical representations R λ , \(\lambda\in\Bbb{C}\) , for the Lobachevsky space ℒ=G/K of dimension n−1 where G=SO0(n−1,1), K=SO(n−1), as the restriction to G of maximal degenerate series representations of the overgroup \(\widetilde{G}=\mathrm{SL}(n,\Bbb{R})\) . We determine explicitly the interaction of Lie operators of \(\widetilde{G}\) with operators intertwining canonical representations and representations of G associated with a cone.

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Authors and Affiliations

  1. Tambov State University, Internatsionalnaya 33, Tambov, 392000, Russia

    V. F. Molchanov

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  1. V. F. Molchanov
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Correspondence to V. F. Molchanov.

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Supported by the Russian Foundation for Basic Research: grants No. 05-01-00074a and No. 05-01-00001a, the Netherlands Organization for Scientific Research (NWO): grant 047-017-015, the Scientific Program “Devel. Sci. Potent. High. School”: project RNP.2.1.1.351 and Templan No. 1.2.02.

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Molchanov, V.F. Canonical Representations on Lobachevsky Spaces: An Interaction with an Overalgebra. Acta Appl Math 99, 321–337 (2007). https://doi.org/10.1007/s10440-007-9169-z

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