Research Catalog

Title

Symplectic fibrations and multiplicity diagrams / Victor Guillemin, Eugene Lerman, Shlomo Sternberg.

Author

Guillemin, Victor, 1937-

Publication

Cambridge ; New York : Cambridge University Press, 1996.

Items in the Library & Off-site

Holdings

Details

Additional Authors

• Lerman, Eugene.
• Sternberg, Shlomo.

Description

xiv, 222 pages : illustrations; 24 cm

Summary

• Multiplicity diagrams can be viewed as schemes for describing the phenomenon of "symmetry breaking" in quantum physics: Suppose the state space of a quantum mechanical system is a Hilbert space V, on which the symmetry group G of the system acts irreducibly. How does this Hilbert space break up when G gets replaced by a smaller symmetry group H? In the case where H is a maximal torus of a compact group a convenient way to record the multiplicities is as integers drawn on the weight lattice of H.
• The subject of this book is the multiplicity diagrams associated with U(n), O(n), and the other classical groups. 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. They develop in detail some themes that were touched on in Symplectic Techniques in Physics (V. Guillemin and S.
• Sternberg, Cambridge University Press, 1984), including the geometry of the moment map, the Duistermaat-Heckman theorem, the interplay between coadjoint orbits and representation theory, and quantization. Students and researchers in geometry and mathematical physics will find this book fascinating.

Subjects

• Representations of groups
• Symplectic groups
• Group theory
• Quantum theory

Bibliography (note)

• Includes bibliographical references (p. 215-219) and index.

Contents

1. Symplectic Fibrations -- 2. Examples of Symplectic Fibrations: The Coadjoint Orbit Hierarchy -- 3. Duistermaat-Heckman Polynomials -- 4. Symplectic Fibrations and Multiplicity Diagrams -- 5. Computations with Orbits -- App. A. Multiplicity Formulas -- App. B. Equivariant Cohomology -- App. C. Update.

ISBN

0521443237 (hc)

LCCN

95045552

OCLC

ocm33333376

Owning Institutions

Columbia University Libraries