Holomorphic induction and the tensor product decomposition of irreducible representations of compact groups. I. SU(n) groups
Klink, W. H. ; Ton-That, T.
Annales de l'I.H.P. Physique théorique, Tome 31 (1979), p. 77-97 / Harvested from Numdam
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@article{AIHPA_1979__31_2_77_0,
     author = {Klink, W. H. and Ton-That, T.},
     title = {Holomorphic induction and the tensor product decomposition of irreducible representations of compact groups. I. $SU(n)$ groups},
     journal = {Annales de l'I.H.P. Physique th\'eorique},
     volume = {31},
     year = {1979},
     pages = {77-97},
     mrnumber = {561916},
     zbl = {0439.22020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPA_1979__31_2_77_0}
}

Klink, W. H.; Ton-That, T. Holomorphic induction and the tensor product decomposition of irreducible representations of compact groups. I. $SU(n)$ groups. Annales de l'I.H.P. Physique théorique, Tome 31 (1979) pp. 77-97. http://gdmltest.u-ga.fr/item/AIHPA_1979__31_2_77_0/

[1] B. Kostant, Trans. Amer. Math. Soc., t. 93, 1959, p. 53 ; A.J. Macfarlane, L. O'Raifeartaigh, and P.S. Rao, J. Math. Phys., t. 8, 1967, p. 536; R.E. Beck, J. Math. Phys., t. 14, 1973, p. 1451; A. Klimyk, Amer. Math. Soc. Transl., Ser. 2, t. 76, 1968, p. 1. | MR 109192

[2] J.P. Elliott, Proc. Roy. Soc., A 245, 1958, p. 128; M. Gellmann, Phys. Rev., t. 125, 1962, p. 1067. | MR 92620 | Zbl 0082.43901

[3] J.J. Deswart, Rev. Mod. Phys., t. 35, 1963, p. 976.

[4] G.W. Mackey, The Theory of Unitary Group Representation (University of Chicago Press, Chicago, 1967), and references cited therein; W.H. Klink, Lectures in Theoretical Physics, edited by K. T. Mahanthappa and W. E. Brittin (Gordon and Breach Science Publishers, Inc., New York, 1969), vol. XI D, p. 43-75. | MR 396826

[5] G. Warner, Harmonic Analysis on Semisimple Lie Group (Springer-Verlag, Berlin, 1972), vol. I. | Zbl 0265.22020

[6] I.M. Gelfand and M.L. Zetlin, Finite Dimensional Representations of the Group of Unimodular Matrices. Dokl. Acad. Nauk. SSR, t. 71, 1950, p. 823-825, Russian; D.P. Zelobenko, Classical Groups. Spectral Analysis of Finite Dimensional Representations, Uspehi Mat. Nauk., t. 27, 1962, p. 53, Russian Math., Surveys, t. 17, 1962, No. 1 ; I.M. Gelfand and M.I. Graev, Finite-dimensional Irreducible Representations of the Unitary Group and the Full Linear Groups and Related Special Functions, Izv. Akad. Nauk. SSSR Ser. Math., t. 29, 1965, p. 1329-1356, English Transl., Amer. Math. Soc. Transl., t. 64, 1967, p. 116-146, MR 34 # 1450. | MR 35774

[7] L.C. Biedenharn, A. Giovannini and J.D. Louck, J. Math. Phys., t. 8, 1967, p. 691 ; L.C. Biedenharn and J.D. Louck, Comm. Math. Phys., t. 8, 1968, p. 89. | MR 235799

[8] E. Cartan, Œuvres Complètes, « Compléments au mémoire sur la géométrie des groupes simples » (Gauthier-Villars, Paris, 1952), partie I, vol. 2, p. 1003-1010. | MR 50516

[9] A. Borel et A. Weil, Séminaire Bourbarki (1953-1954).

Exposé 100 par J.P. Serre, Représentations linéaires et espaces homogènes Kähleriens des groupes de Lie compacts (Secrétariat Math., Paris, 1959) ; R. Bott, Ann. of Math., t. 66, 1957, p. 203. | Numdam | Zbl 0121.16203

[10] H. Weyl, The Classical Groups. Their Invariants and Representations, 2d ed. (Princeton Univ. Press, Princeton, N. J., 1946). | MR 1488158

[11] T. Ton-That, Trans. Amer. Math. Soc., t. 216, 1976, p. 1-46. | MR 399366 | Zbl 0287.22014

[12] J.D. Louck, Amer. J. Phys., t. 38, 1970, p. 3-42. | MR 578897

[13] W.H. Klink and T. Ton-That, Orthogonal Polynomial Bases for Holomorphically Induced Representations of the General Linear Groups, Ann. Inst. Henri Poincaré, Vol. XXXI, n° 2, 1979, p. 99-113. | Numdam | MR 561917 | Zbl 0439.22021

W.H. Klink et T. Ton-That, Construction Explicite Non-Itérative des Bases de GL(n, C)-Modules, Comptes Rendus de l'Académie des Sciences, Séance du 16 juillet 1979.

[14] J.D. Louck and L.C. Biedenharn, The Null Space Concept in Implementing Unitary Symmetry, Revista Mexicana de Fiscia, t. 23, 1974, p. 221-242, and references cited therein.