Boson basis realization for shell-model fermion problem

The boson basis for the fermion shell-model problem has been realized over a representation space V_{n(n - 1)/2} of the unitary group U(n(n - l)/2). A contraction of this space was found to yield the generator algebra of U(n). Based on this result it is shown that the transformations induced by the Dyson-mapped boson Hamiltonian on the Dyson boson basis are identical to the corresponding transformations by the fermion Hamiltonian on the shell-model basis.