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Prog. Theor. Phys. Vol. 40 No. 5 (1968) pp. 1137-1142
Proof of the Factorizability Theorem Conjectured by Sciarrino and Toller
Noboru Nakanishi
Research Institute for Mathematical Sciences, Kyoto University, Kyoto
(Received June 17, 1968)
Abstract:
A general proof of a symmetry property of the residues of the transformation function between irreducible representations of SU(2) and SU(1, 1) which is encountered in the decomposition of the principal series of the SL(2, C) functions is presented.
URL :
http://ptp.ipap.jp/link?PTP/40/1137/
DOI : 10.1143/PTP.40.1137
References:
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A. Sciarrino and M. Toller, J. Math. Phys. 8 (1967), 1252[CrossRef].
- I. M. Gel'fand, R. A. Minlos and Z. Ya. Shapiro, Representations of the Rotation and Lorentz Groups and Their Applications (Pergamon Press, Oxford, 1963, English translation), p. 85.
- V. Bargmann, Ann. Math. 48 (1947), 568.
- R. Delbourgo, K. Koller and P. Mahanta, Nuovo Cim. A 52 (1967), 1254.
- D. A. Akyeampong, J. F. Boyce and M. A. Rashid, Nuovo Cim. A 53 (1968), 737.
- L. Schwartz, Théorie des Distributions (Hermann & Cle, Paris, 1950), Chap. II, §2.
- M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (National Bureau of Standards, Washington D. C., 1964), p. 559.
