Abstract
The methods of the generating functions for invariants (covariants) of classical groups can be used for the solution of a number of problems connected with the construction of the bases of the wavefunctions and effective Hamiltonians. In particular, the method is applied to the decomposition U(6) contains/implies SU(3)*SU(2) contains/implies SO(3), and the following generating functions are obtained: (i) the generating function for the SU(3) basis of Bargmann-Moshinsky; (ii) the generating function for the number of invariants in the interacting vector boson model; (iii) the generating function for the classification of the states in the scheme SU(3) contains/implies SO(3).
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