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Canonical Representations and Overgroups for Hyperboloids of One Sheet and Lobachevsky Spaces

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Abstract

We define canonical representations for the hyperboloid of one sheet \(\mathcal{X}=G/H\) and for the Lobachevsky space ℒ=G/K where G=SO0(1,n−1), H=SO0(1,n−2) and K=SO(n−1), as the restriction to G of representations associated with a cone of overgroups \(\widetilde{G}=\mathrm{SO}_{0}(2,n-1)\) and \(\widetilde{G}=\mathrm{SO}_{0}(1,n)\) for \(\mathcal{X}\) and ℒ respectively. 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, 392622, Tambov, 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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Mathematics Subject Classifications (2000)

43A85, 22E46, 53D55.

V. F. Molchanov: Supported by grants of the Netherlands Organization for Scientific Research (NWO): 047-008-009, the Russian Foundation for Basic Research (RFBR): 01-01-00100-a, the Minobr RF: E00-1.0-156, the NTP “Univ. Rossii”: ur04.01.037.

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Molchanov, V.F. Canonical Representations and Overgroups for Hyperboloids of One Sheet and Lobachevsky Spaces. Acta Appl Math 86, 115–129 (2005). https://doi.org/10.1007/s10440-005-0465-1

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