Abstract
The paper is the continuation of a previous one [ Physica Scripta 22 (1980), 545–555] devoted to quadrupling in the shell model. We consider here a simple model of the ten- dimensional quasi-spin Lie algebra which is spectrum generating for the quadrupling Hamiltonian. The model allows us to investigate many concrete aspects of the theory of linear representations of the quasi-spin algebra. In particular, we present an explicit construction of the irreducible representation module for the finite dimensional representations, and we consider the direct product of the such irreducible modules.
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