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Izv. Akad. Nauk SSSR Ser. Mat., 1979, Volume 43, Issue 4, Pages 860–891 (Mi izv1735)  

This article is cited in 15 scientific papers (total in 15 papers)

Tensor products of unitary representations of the three-dimensional Lorentz group

V. F. Molchanov


Abstract: The author obtains a decomposition into irreducible representations of the tensor product of any two irreducible unitary representations of the group $SO_0(1,2)$. An explicit construction of this decomposition is given, and the corresponding Plancherel measure is found.
Bibliography: 13 titles.

Full text: PDF file (2598 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1980, 15:1, 113–143

Bibliographic databases:

UDC: 513.8
MSC: Primary 22E43; Secondary 22E45
Received: 25.09.1978

Citation: V. F. Molchanov, “Tensor products of unitary representations of the three-dimensional Lorentz group”, Izv. Akad. Nauk SSSR Ser. Mat., 43:4 (1979), 860–891; Math. USSR-Izv., 15:1 (1980), 113–143

Citation in format AMSBIB
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\by V.~F.~Molchanov
\paper Tensor products of unitary representations of the three-dimensional Lorentz group
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1979
\vol 43
\issue 4
\pages 860--891
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=548507}
\zmath{https://zbmath.org/?q=an:0448.22010|0438.22007}
\transl
\jour Math. USSR-Izv.
\yr 1980
\vol 15
\issue 1
\pages 113--143
\crossref{https://doi.org/10.1070/IM1980v015n01ABEH001191}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1980LB83500005}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. F. Molchanov, “Harmonic analysis on pseudo-Riemannian symmetric spaces of the group $SL(2,\mathbf R)$”, Math. USSR-Sb., 46:4 (1983), 493–506  mathnet  crossref  mathscinet  zmath
    2. Yu. A. Neretin, “The restrictions of functions holomorphic in a domain to curves lying on its boundary, and discrete $\operatorname{SL}_2(\mathbb R)$-spectra”, Izv. Math., 62:3 (1998), 493–513  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. G. van Dijk, V.F. Molchanov, “The Berezin form for rank one para-Hermitian symmetric spaces”, Journal de Mathématiques Pures et Appliquées, 77:8 (1998), 747  crossref  elib
    4. G. Van Dijk, V.F. Molchanov, “Tensor products of maximal degenerate series representations of the group SL(n, R)”, Journal de Mathématiques Pures et Appliquées, 78:1 (1999), 99  crossref  elib
    5. Yu. A. Neretin, “The action of an overalgebra on the Plancherel decomposition and shift operators in the imaginary direction”, Izv. Math., 66:5 (2002), 1035–1046  mathnet  crossref  crossref  mathscinet  zmath  elib
    6. Yurii A. Neretin, “Plancherel Formula for Berezin Deformation of L2 on Riemannian Symmetric Space”, Journal of Functional Analysis, 189:2 (2002), 336  crossref
    7. J. H. Bernstein, A. Reznikov, “Estimates of automorphic functions”, Mosc. Math. J., 4:1 (2004), 19–37  mathnet  mathscinet  zmath
    8. André van Tonder, “Cohomology and decomposition of tensor product representations of”, Nuclear Physics B, 677:3 (2004), 614  crossref
    9. Yu. A. Neretin, “Some Continuous Analogs of the Expansion in Jacobi Polynomials and Vector-Valued Orthogonal Bases”, Funct. Anal. Appl., 39:2 (2005), 106–119  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. Yu. A. Neretin, “Perturbations of Jacobi polynomials and piecewise hypergeometric orthogonal systems”, Sb. Math., 197:11 (2006), 1607–1633  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. J. Math. Sci. (N. Y.), 141:4 (2007), 1452–1478  mathnet  crossref  mathscinet  zmath  elib
    12. Michael Pevzner, “Rankin–Cohen Brackets and Associativity”, Lett Math Phys, 85:2-3 (2008), 195  crossref  mathscinet  isi
    13. Michael Pevzner, “Covariant quantization: spectral analysis versus deformation theory”, Jpn J Math, 3:2 (2008), 247  crossref  mathscinet  isi  elib
    14. Ralf Beckmann, Jean-Louis Clerc, “Singular invariant trilinear forms and covariant (bi-)differential operators under the conformal group”, Journal of Functional Analysis, 2012  crossref
    15. Danijel Jurman, Harold Steinacker, “2D fuzzy anti-de Sitter space from matrix models”, J. High Energ. Phys, 2014:1 (2014)  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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