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Klink, W. H.; Ton-That, T.

Matrix elements and highest weight Wigner coefficients of GL(n,C). (English) Zbl 0488.22041

Ann. Inst. Henri Poincaré, Nouv. Sér., Sect. A 36, 225-237 (1982).
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Cited in 5 Documents

MSC:

22E70 Applications of Lie groups to the sciences; explicit representations
22E30 Analysis on real and complex Lie groups
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations

Keywords:

linear group; irreducible representation; tensor product; matrix coefficients; highest weight Wigner coefficients; fundamental representations
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References:

[1] I.M. Gelfand and M.I. Graev , Finite-dimensional irreducible representations of the unitary group and the full linear group and related special functions . Izv. Akad. Nauk. S. S. S. R. Ser. Math. , t. 29 , 1965 , p. 1329 - 1356 ; English transl., Amer. Math. Soc. Transl. , t. 64 , 1967 , p 116 - 146 . MR 201568 | Zbl 0185.21701 · Zbl 0185.21701
[2] A.U. Klimyk , Lett. Math. Phys. , t. 3 , 1979 , p. 315 . MR 545409 | Zbl 0418.22018 · Zbl 0418.22018 · doi:10.1007/BF01821852
[3] W.H. Klink and T. Ton-That , Ann. Inst. H. Poincaré , Ser. A , t. 31 , 1979 . p. 77 - 79 . Numdam | Zbl 0439.22020 · Zbl 0439.22020
[4] W.H. Klink and T. Ton-That , C. R. Acad. Sci. , Ser. B , t. 289 , 1979 , p. 115 - 118 .
[5] L.C. Biedenharn and J.D. Louck , Comm. Math. Phys. , t. 8 , 1968 , p. 89 ; M.K.F. Wong , J. Math. Phys. , t. 20 , 1979 , p. 2391 , and references cited therein. It should be noted in these references the multiplicity free Wigner coefficients are computed inductively. MR 235799
[6] Hou Pei-Yu , Scientia Sinica , t. 15 , n^\circ 6 , 1966 , p. 763 - 772 . MR 209397 | Zbl 0149.27403 · Zbl 0149.27403
[7] W.H. Klink and T. Ton-That , Ann. Inst. H. Poincaré , Ser. A , t. 31 , 1979 , p. 99 - 113 . Numdam | MR 561917 | Zbl 0439.22021 · Zbl 0439.22021
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