  Degeneracies in the energy spectra of physical systems are commonly
considered to be either of accidental character or induced by symmetries of the
Hamiltonian. We develop an approach to explain degeneracies by tracing them
back to symmetries of an isospectral effective Hamiltonian derived by subsystem
partitioning. We provide an intuitive interpretation of such latent symmetries
by relating them to corresponding local symmetries in the powers of the
underlying Hamiltonian matrix. As an application, we relate the degeneracies
induced by the rotation symmetry of a real Hamiltonian to a non-abelian latent
symmetry group. It is demonstrated that the rotational symmetries can be broken
in a controlled manner while maintaining the underlying more fundamental latent
symmetry. This opens up the perspective of investigating accidental
degeneracies in terms of latent symmetries.
