Orthogonal polynomial bases for holomorphically induced representations of the general linear groups

W. H. Klink; T. Ton-That

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

  • Volume: 31, Issue: 2, page 99-113
  • ISSN: 0246-0211

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Klink, W. H., and Ton-That, T.. "Orthogonal polynomial bases for holomorphically induced representations of the general linear groups." Annales de l'I.H.P. Physique théorique 31.2 (1979): 99-113. <http://eudml.org/doc/76048>.

@article{Klink1979,
author = {Klink, W. H., Ton-That, T.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {GL(n); holomorphically induced representations; polynomial bases},
language = {eng},
number = {2},
pages = {99-113},
publisher = {Gauthier-Villars},
title = {Orthogonal polynomial bases for holomorphically induced representations of the general linear groups},
url = {http://eudml.org/doc/76048},
volume = {31},
year = {1979},
}

TY - JOUR
AU - Klink, W. H.
AU - Ton-That, T.
TI - Orthogonal polynomial bases for holomorphically induced representations of the general linear groups
JO - Annales de l'I.H.P. Physique théorique
PY - 1979
PB - Gauthier-Villars
VL - 31
IS - 2
SP - 99
EP - 113
LA - eng
KW - GL(n); holomorphically induced representations; polynomial bases
UR - http://eudml.org/doc/76048
ER -

References

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  1. [1] H. Boerner, Representations of Groups, North-Holland Publish-ing Co., Amsterdam, 1970. MR272911
  2. [2] I.M. Gelfand and M.L. Žetlin, Finite-dimensional representations of the group of unimodular matrices, Dokl. Acad. Nauk. SSSR, t. 71, 1950, p. 825-828 (Russian) MR 12, 9. MR35774
  3. [3] 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., (2), t. 64, 1967, p. 116-146, MR 34 # 1450. Zbl0185.21701MR201568
  4. [4] W.H. Klink and T. Ton-That, Holomorphic induction and the tensor product decomposition of irreducible representations of compact groups. I. SU(n) groups, Ann. Inst. Henri Poincaré, Vol. XXXI, n° 2, 1979, p. 77-97. Zbl0439.22020MR561916
  5. [5] T. Ton-That, Lie group reprensentations and harmonic polynomials of a matrix variable, Trans. Amer. Math. Soc., t. 216, 1976, p. 1-46, MR 53,3 # 3210. Zbl0287.22014MR399366
  6. [6] G. Warner, « Harmonic Analysis on Semisimple Lie Groups, I », Springer-Verlag, Berlin, 1972. Zbl0265.22020
  7. [7] D.P. Želobenko, Compact Lie groups and their representations, « Nauka », Moscow, 1970; English transl., Transl. Math. Monographs, vol. 40, Amer. Math. Soc., Providence, R. I., 1973. MR473098

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