Geodesic
Clebsch--Gordan coefficients of the Lorentz group
Teoretičeskaâ i matematičeskaâ fizika, Tome 16 (1973) no. 3, pp. 360-367

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Gel'fand and Graev's results [1] are used to show that the homogeneous components of the one-particle helical state with zero mass $|k\lambda;\;\rho>(k^2=0)$ form the space of the irreducible representation $\chi(i\rho+\lambda,i\rho-\lambda)$ of the Lorentz group. In a spherical coordinate system it is identical with the space of functions $f(u)$ on the group $U$ of unitary matrices. A decomposition of the space of the direct product of these representations into invariant subspaces is obtained as well as an integral representation for the Clebsch–Gordancoefficients in a canonical basis. 
@article{TMF_1973_16_3_a8,
     author = {I. A. Verdiev},
     title = {Clebsch--Gordan coefficients of the {Lorentz} group},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {360--367},
     publisher = {mathdoc},
     volume = {16},
     number = {3},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1973_16_3_a8/}
}
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I. A. Verdiev. Clebsch--Gordan coefficients of the Lorentz group. Teoretičeskaâ i matematičeskaâ fizika, Tome 16 (1973) no. 3, pp. 360-367. http://geodesic.mathdoc.fr/item/TMF_1973_16_3_a8/