Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of these hidden symmetries depends upon the realization of the Hamiltonian.

• Received 12 December 1996

DOI:https://doi.org/10.1103/PhysRevLett.79.537