THE THEORY OF REPRESENTATIONS OF GROUPS SO0 2; 1 AND ISO 2; 1 . WIGNER COEFFICIENTS OF THE GROUP SO0 2; 1
This paper is devoted to the representations of the groups SO 2; 1 and ISO 2; 1 . Those groups have an important role in cosmology, elementary particle theory and mathematical physics. Irreducible unitary representations of the principal continuous and supplementary as well as discrete series were obtained. Explicit expressions for spherical functions of the group SO0 2; 1 are obtained through the Gauss hypergeometric functions. The Wigner coecients of the group SO0 2; 1 were computed and their explicit expressions using the bilateral series were represented. The results could be used to study the non-degenerate representations of the de Sitter group SO 3; 2 .
Keywords:
Bilateral series, ISO0 2, 1 and SO0 2, 1 groups, de Sitter group SO 3, 2, Wigner coecients unitary irreducible representations.,
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- Alhaidari A. D., (2002), arXiv:math-ph/0112004, p.14.
- Vilasi G., Vitale P., (2002), arXiv:gr-qc/0202018v.1, p.10.
- Schmutzer E., (1980), Exact solutions of the Einsteins field equations, Berlin.
- Oblak B., (2017), BMS Particles in Three Dimensions, Springer, p.461.
- Gelfand I. M., Graev M. I., Vilenkin H. Y., (1962), Integral geometry and associated questions of the theory of representation, FM., p.656 (In Russian).
- Vilenkin N.Y, (1965), Special functions and theory of groups representation, Nauka, P.588.
- Zhelobenko D.P., Stern A.I., (1983), Representations of Lie Groups, Nauka, (in Russian).
- Treves F., (1967), Topological Vector Spaces, Distributions and Kernels, Purdue University, Indiana.
- Bateman G., Erd´elyi A., (1973), Higher transcendental functions, Nauka, V.1, p.294, (In Russian).
- Gelfand I. M., Shilov G. E., (1959), Generalization of the function and operations on them (Generalized Functions, vol. 1, 2nd edition) - Physmatlit, p.471, (In Russian).
- Slater L. J., (1966), Generalized hypergeometric functions Cambridge, p.273.
- Rajabov B. A., (2018), TWMS J. App. Eng. Math. V.8, pp.32-43.
- Barut A. O., Raczka R., (1977), Theory of Group Representations and Applications, Warsaw.
- Bekaert X., Skvortsov E., (2017), arXiv:1708.01030v2 [hep-th], p.33.
- B. A. Rajabov for the photography and short autobiography, see TWMS J. App. Eng. Math. V.8, N.1, 2018.
- ISSN: 2146-1147
- Başlangıç: 2010
- Yayıncı: Turkic World Mathematical Society
Sayıdaki Diğer Makaleler
T. TUNÇ, H. BUDAK, M. Z. SARİKAYA