Holomorphic induction and the tensor product decomposition of irreducible representations of compact groups. I. S U ( n ) groups

W. H. Klink; T. Ton-That

Annales de l'I.H.P. Physique théorique (1979)

  • Volume: 31, Issue: 2, page 77-97
  • ISSN: 0246-0211

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Klink, W. H., and 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 31.2 (1979): 77-97. <http://eudml.org/doc/76047>.

@article{Klink1979,
author = {Klink, W. H., Ton-That, T.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {SU(n); holomorphic induction; tensor products; polynomial functions; Mackey induced representation theory},
language = {eng},
number = {2},
pages = {77-97},
publisher = {Gauthier-Villars},
title = {Holomorphic induction and the tensor product decomposition of irreducible representations of compact groups. I. $SU(n)$ groups},
url = {http://eudml.org/doc/76047},
volume = {31},
year = {1979},
}

TY - JOUR
AU - Klink, W. H.
AU - Ton-That, T.
TI - Holomorphic induction and the tensor product decomposition of irreducible representations of compact groups. I. $SU(n)$ groups
JO - Annales de l'I.H.P. Physique théorique
PY - 1979
PB - Gauthier-Villars
VL - 31
IS - 2
SP - 77
EP - 97
LA - eng
KW - SU(n); holomorphic induction; tensor products; polynomial functions; Mackey induced representation theory
UR - http://eudml.org/doc/76047
ER -

References

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  2. [2] J.P. Elliott, Proc. Roy. Soc., A245, 1958, p. 128; M. Gellmann, Phys. Rev., t. 125, 1962, p. 1067. Zbl0082.43901MR92620
  3. [3] J.J. Deswart, Rev. Mod. Phys., t. 35, 1963, p. 976. 
  4. [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. MR396826
  5. [5] G. Warner, Harmonic Analysis on Semisimple Lie Group (Springer-Verlag, Berlin, 1972), vol. I. Zbl0265.22020
  6. [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. MR35774
  7. [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. MR235799
  8. [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. MR50516
  9. [9] A. Borel et A. Weil, Séminaire Bourbarki (1953-1954). 
  10. 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. Zbl0121.16203
  11. [10] H. Weyl, The Classical Groups. Their Invariants and Representations, 2d ed. (Princeton Univ. Press, Princeton, N. J., 1946). Zbl1024.20502MR1488158
  12. [11] T. Ton-That, Trans. Amer. Math. Soc., t. 216, 1976, p. 1-46. Zbl0287.22014MR399366
  13. [12] J.D. Louck, Amer. J. Phys., t. 38, 1970, p. 3-42. MR578897
  14. [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. Zbl0439.22021MR561917
  15. 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. 
  16. [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. 

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