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Generalized vector coherent state theory of sp(2N, ℝ) vector operators and of sp(2N, ℝ) ⊃ u(N) reduced Wigner coefficients

par Quesne, Christiane
Référence Journal of Physics A: Mathematical and General, 24, 12, page (2697-2714)
Publication Publié, 1991-06

Article révisé par les pairs

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Résumé :

sp(2N, ℝ) ⊃ u(N) reduced Wigner coefficients coupling a positive discrete series unitary irreducible representation with the 2N-dimensional non-unitary irreducible representation characterized by (1) are evaluated by making use of generalized vector coherent state techniques. General formulae are given in terms of the K-matrix elements of vector coherent state theory and of some u(N) 6j or 9j-type recoupling coefficients. Explicit analytic expressions are obtained in some important special cases. Such results should allow a determination of wsp(2N, ℝ) ≈ w (N)⊕sp(2N, ℝ) and osp(P/2N, ℝ) matrix representations to be completed, because both the w(N) generators and the osp(P/2N, ℝ) odd generators transform under the sp(2N, ℝ) irrep(I). © 1991 IOP Publishing Ltd.