A short review of the plethysm technique aiming to its application in finding branching rules for the reduction of an irreducible representation of a group under the restriction to one of its subgroups is given. The algebraic structure of the interacting boson model and some of its extensions is given together with the branching rules needed to classify their basis states, obtained by the use of plethysms.

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The application of the Restricted Dynamics Approach in nuclear theory, based on the approximate solution of many-particle Schrödinger equation, which accounts for all conservation laws in many-nucleon system, is discussed. The Strictly Restricted Dynamics Model is used for the evaluation of binding energies, level schemes, E2 and M1 transition probabilities as well as the electric quadrupole and magnetic dipole momenta of light α-cluster type nuclei in the region 4 ≤ A ≤ 40. The parameters of effective nucleon-nucleon interaction potential are evaluated from the ground state binding energies of doubly magic nuclei 4 He , 16 O and 40 Ca .