Advertisement

Siberian Mathematical Journal

, Volume 58, Issue 6, pp 990–1003 | Cite as

On the Matrices of Clebsch–Gordan Coefficients

Article
  • 12 Downloads

Abstract

We consider the matrices of Clebsch–Gordan coefficients. It turns out that these matrices are convenient in order to state, prove, and use many facts of the theory of representations of the groups SO(3) and SU(2).

Keywords

representations of SO(3) and SU(2) Clebsch–Gordan coefficient harmonic polynomial 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Vilenkin N. Ya., Special Functions and Representation Theory of Groups [Russian], Nauka, Moscow (1991).CrossRefMATHGoogle Scholar
  2. 2.
    Smorodinskii Y. A. and Shelepin L. A., “Clebsch–Gordan coefficients, viewed from different sides,” Soviet Physics Uspekhi, vol. 15, no. 1, 1–24 (1972).MathSciNetCrossRefGoogle Scholar
  3. 3.
    Shelepin L. A., “Calculus of Clebsch–Gordan coefficients and its physical applications,” Proc. (Trudy) Lebedev Phys. Inst., vol. 70, 1–114 (1975).Google Scholar
  4. 4.
    Godunov S. K. and Mikhaĭlova T. Yu., Representations of the Rotation Group and Spherical Functions [Russian], Nauchnaya Kniga, Novosibirsk (1998).Google Scholar
  5. 5.
    Godunov S. K. and Gordienko V. M., “Complicated structures of Galilean-invariant conservation laws,” J. Appl. Mech. Tech. Phys., vol. 43, no. 2, 175–189 (2002).MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Godunov S. K. and Gordienko V. M., “The Clebsch–Gordan coefficients with respect to various bases for unitary and orthogonal representations of SU(2) and SO(3),” Sib. Math. J., vol. 45, no. 3, 443–458 (2004).CrossRefMATHGoogle Scholar
  7. 7.
    Gelfand I. M., Minlos R. A., and Shapiro Z. Ya., Representations of the Rotation Group and the Lorentz Group, and Their Applications [Russian], Fizmatgiz, Moscow (1958).Google Scholar
  8. 8.
    Mikhaĭlova T. Yu., Four Lectures on the Theory of Representations of Rotation Groups [Russian], Novosibirsk Univ., Novosibirsk (2010).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirsk State UniversityNovosibirskRussia

Personalised recommendations