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Zapiski Nauchnykh Seminarov POMI, 2006, Volume 331, Pages 91–124
(Mi znsl252)
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Canonical representations on two-sheeted hyperboloids
V. F. Molchanov Tambov State University
Abstract:
The two-sheeted hyperboloid $\mathcal L$ in $\mathbb R^n$ can be identified with
the unit sphere $\Omega$ in $\mathbb R^n$ without the equator. Canonical
representations of the group $G=\mathrm{SO}_0(n-1,1)$ on $\mathcal L$ are defined as
the restrictions to $G$ of the representations of the overgroup
$\widetilde G=\mathrm{SO}_0(n,1)$ associated with a cone. They act on functions and distributions on the sphere $\Omega$. We decompose these canonical representations into irreducible constituents and decompose the Berezin
form.
Received: 17.05.2006
Citation:
V. F. Molchanov, “Canonical representations on two-sheeted hyperboloids”, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XIV, Zap. Nauchn. Sem. POMI, 331, POMI, St. Petersburg, 2006, 91–124; J. Math. Sci. (N. Y.), 141:4 (2007), 1432–1451
Linking options:
https://www.mathnet.ru/eng/znsl252 https://www.mathnet.ru/eng/znsl/v331/p91
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Abstract page: | 341 | Full-text PDF : | 102 | References: | 78 |
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