Skip to main content
Log in

Decomposition of a tensor square of a representation of the supplementary series of the unimodular group of real matrices of second order

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Literature Cited

  1. L. Pukansky, “On the Kronecker products of irreducible representations of the 2×2 real unimodular group. I,” Trans. Am. Math. Soc.,100, No. 1, 116–152 (1961).

    Google Scholar 

  2. F. A. Berezin, “General concept of quantization,” Preprint JTP-74-20E, Inst. Teor. Fiz., Akad. Nauk Ukr. SSR (1974).

  3. V. F. Molchanov, “Representations of a pseudoorthogonal group, connected by a cone,” Mat. Sb.,81(123), No. 3, 358–375 (1970).

    Google Scholar 

  4. N. Mukunda, “Unitary representations of the Lorentz group: reduction of the supplementary series under a noncompact subgroup,” J. Math. Phys.,9, No. 3, 417–431 (1968).

    Google Scholar 

  5. A. M. Vershik, I. M. Gel'fand, and M. I. Graev, “Representation of the group SL(2, R) where R is a ring of functions,” Usp. Mat. Nauk,28, No. 5, 83–128 (1973).

    Google Scholar 

  6. N. Ya. Vilenkin, Special Functions and the Theory of Group Representation [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  7. I. M. Gel'fand and G. E. Shilov, Functions and Generalized Function Spaces, Academic Press (1968).

  8. I. M. Gel'fand and G. E. Shirov, Basic Spaces and Generalized Functions [in Russian], Fizmatgiz, Moscow (1958).

    Google Scholar 

  9. N. Bourbaki, Integration, Addison-Wesley.

  10. A. Tengstrand, “Distributions invariant under an orthogonal group of arbitrary signature,” Math. Scand.,8, 201–218 (1960).

    Google Scholar 

  11. G. Beitman and A. Yerdeii, Advanced Transcendent Functions (Hypergeometric Function of the Legendre Function) [in Russian], Nauka, Moscow (1965).

    Google Scholar 

  12. N. Dunford and J. T. Schwartz, Linear Operators, Pt. 2, Spectral Theory of Self-Adjoint Operators in Hilbert Space, Wiley.

  13. F. A. Berezin and M. A. Shubin, Lecture on Quantum Mechanics [in Russian], Izd. MGU, Moscow (1972).

    Google Scholar 

Download references

Authors

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, Vol. 18, No. 1, pp. 174–188, January–February, 1977.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Molchanov, V.F. Decomposition of a tensor square of a representation of the supplementary series of the unimodular group of real matrices of second order. Sib Math J 18, 128–138 (1977). https://doi.org/10.1007/BF00966957

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00966957

Keywords

Navigation