Generalized vector coherent state theory of sp(2N,R) vector operators and of sp(2N,R) contains/implies u(N) reduced Wigner coefficients
C. Quesne · Journal of Physics A Mathematical and General · 1991
sp(2N,R) contains/implies 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) approximately=w (N)(+)p(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(1).