We analyze the occurrence of dynamically equivalent Hamiltonians in the
parameter space of general many-body interactions for quantum systems,
particularly those that conserve the total number of particles. As an
illustration of the general framework, the appearance of parameter symmetries
in the interacting boson model-1 and their absence in the Ginocchio SO(8)
fermionic model are discussed.Comment: 8 pages, REVTeX, no figur