  We show that partial dynamical symmetries (PDS) can occur at critical-points
of quantum phase transitions, in which case, underlying competing symmetries
are conserved exactly by a subset of states, and mix strongly in other states.
Several types of PDS are demonstrated with the example of critical-point
Hamiltonians for first- and second-order transitions in the framework of the
interacting boson model, whose dynamical symmetries correspond to different
shape-phases in nuclei.
