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A central theme in Iachello's quest for understanding simple ordered patternsin complex quantum systems, is the concept of dynamical symmetry. Relying onhis seminal contributions, we present further generalization of this notion tothat of partial dynamical symmetry (PDS), for which solvability and goodquantum numbers are maintained by only a subset of states. Hamiltonians with asingle PDS and multiple PDSs are constructed explicitly and their relevance tonuclear structure is discussed.

Dynamical Symmetries and Beyond: Lessons and Advances