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Zap. Nauchn. Sem. POMI, 2006, Volume 331, Pages 91–124 (Mi znsl252)  

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.

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English version:
Journal of Mathematical Sciences (New York), 2007, 141:4, 1432–1451

Bibliographic databases:

UDC: 517.98
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

Citation in format AMSBIB
\Bibitem{Mol06}
\by V.~F.~Molchanov
\paper Canonical representations on two-sheeted hyperboloids
\inbook Representation theory, dynamical systems, combinatorial and algoritmic methods. Part~XIV
\serial Zap. Nauchn. Sem. POMI
\yr 2006
\vol 331
\pages 91--124
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl252}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2251344}
\zmath{https://zbmath.org/?q=an:1118.22006}
\elib{http://elibrary.ru/item.asp?id=9172488}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2007
\vol 141
\issue 4
\pages 1432--1451
\crossref{https://doi.org/10.1007/s10958-007-0051-3}
\elib{http://elibrary.ru/item.asp?id=13548355}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846799323}


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