Coexisting partial dynamical symmetries and multiple shapes

We present an algebraic procedure for constructing Hamiltonians with several distinct partial dynamical symmetries (PDSs), of relevance to shape-coexistence phenomena. The procedure relies on a spectrum generating algebra encompassing several dynamical symmetry (DS) chains and a coherent state which assigns a particular shape to each chain. The PDS Hamiltonian maintains the DS solvability and quantum numbers in selected bands, associated with each shape, and mixes other states. The procedure is demonstrated for a variety of multiple quadrupole shapes in the framework of the interacting boson model of nuclei.