Abstract
A method for evaluation of matrix elements of unitary irreducible representations of compact Lie groups is formulated. matrix elements of some representations of the group SO(p+q) in the SO(p) ⊗ SO(q) basis and of the group U(p) ⊗ U(p) in the U(p) basis (diagonal imbedding) are given.
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References
WarnerG., Harmonic Analysis on Semisimple Lie Groups vol. 1, Springer, Berlin, New York, 1972, pp. 75, 78.
BarutA.O. and RaczkaR., Theory of Group Representations and Applications, PWN, Warsaw, 1977.
LepowskyJ. and WallachN.R., Trans. Amer. Math. Soc. 184, 223 (1973).
KlimykA.U., Matrix Elements and Clebsch-Gordon Coefficients of Group Representations, Naukova Dumka, Kiev, 1979 (in Russian), p. 13.
VilenkinN.Ja., Special Functions and the Theory of Group Representations, Amer. Math. Soc., Providence, 1968, pp. 465, 520.
KlimykA.U. and GavrilikA.M., J. Math. Phys. 20, 1624 (1979).
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Klimyk, A.U. Representation for matrix elements of compact Lie groups. Lett Math Phys 4, 399–404 (1980). https://doi.org/10.1007/BF00417407
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DOI: https://doi.org/10.1007/BF00417407