Twentieth Century Multiplicity

The book describes the ways in which American thinkers and artists in the first two decades of the twentieth century challenged notions that a single principle explained all relevant phenomena, opting instead for a pluralistic world in which many truths, goods, and beauties coexisted.

Symplectic Fibrations and Multiplicity Diagrams

Multiplicity diagrams can be viewed as schemes for describing the phenomenon of "symmetry breaking" in quantum physics. The subject of this book is the multiplicity diagrams associated with the classical groups U(n), O(n), etc. It presents such topics as asymptotic distributions of multiplicities, hierarchical patterns in multiplicity diagrams, lacunae, and the multiplicity diagrams of the rank 2 and rank 3 groups. The authors take a novel approach, using the techniques of symplectic geometry.