On the Regge symmetries of the 3j symbols of SU(2)
Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 7 (1967) no. 4, pp. 353-366. 
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     author = {Flamand, G.},
     title = {On the {Regge} symmetries of the $3j$ symbols of $SU \, (2)$},
     journal = {Annales de l'institut Henri Poincar\'e. Section A, Physique Th\'eorique},
     pages = {353--366},
     publisher = {Gauthier-Villars},
     volume = {7},
     number = {4},
     year = {1967},
     mrnumber = {223139},
     zbl = {0241.20035},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPA_1967__7_4_353_0/}
}
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Flamand, G. On the Regge symmetries of the $3j$ symbols of $SU \, (2)$. Annales de l'institut Henri Poincaré. Section A, Physique Théorique, Tome 7 (1967) no. 4, pp. 353-366. http://archive.numdam.org/item/AIHPA_1967__7_4_353_0/

[1] T. Regge, Nuovo Cim., t. 10, 1958, p. 296.

[2] J. Schwinger, unpublished, 1952. U. S. Atom. Energy Comm. NYO-3071 (Reprinted in Quantum Theory of Angular Momentum, edited by L. C. Biedenharn and H.Van Dam. Academic Press, 1965).

V. Bargmann, Rev. Mod. Phys., t. 34, 1962, p. 829. Some acquaintance with these beautiful papers is expected from the reader. | MR | Zbl

[4] J.R. Derome, J. Math. Phys., t. 7, 1966, p. 612. It is proved in this paper that the 3j symbols of any compact group do have the class I symmetries except when the three representations are equivalent. In that case a general criterion for their existence and a counter example are given. | MR | Zbl

[5] Another instance of this property can be found in A. J. DRAGT, J. Math. Phys., t. 6, 1965, p. 533, section 6 B, in a somewhat different context though.

[7] J.R. Derome, Orsay preprint, TH/138.

[8] The Lie algebra SO*(2n) , is described inS. Helgason, Differential Geometry and Symmetric Spaces, Academic Press, 1962, p. 341.