Proceedings of a symposium held in Landesbildungszentrum Schloss Hofen, Lochau, Vorarlberg, Austria, July 30-August 3, 1990

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Dynamical Symmetries of Relativistic Two - and Many Body Systems.- Algebraic Treatment of Multistep Processes in Electron-Molecule Scattering.- Symmetry, Constitutive Laws of Bounded Smoothly Deformable Media and Neumann Problems.- Imitation of Symmetries in Local Quantum Field Theory.- Representations of Quantum Groups.- Algebras and Symmetries - Quantum Mechanical Symmetry Breaking.- q-Analysis and Quantum Groups.- Orthogonal Polynomials and Coherent States.- Algebraic Model for Molecular Electronic Spectra.- Highest Weight Unitary Modules for Non-Compact Groups and Applications to Physical Problems.- Scattering Theory and the Group Representation Matrix.- Predicting "Anyons": The Origins of Fractional Statistics in Two-Dimensional Space.- The Role of Parabose-Statistics in Making Abstract Quantum Theory Concrete.- On Quantized Verma Modules.- The Role of Spectrum Generating Algebras and Dynamic Symmetries in Molecular Physics.- O(4) Symmetry and Angular Momentum Theory in Four Dimensions.- Representations of the Quantum Algebras Uq(su(2)) and Uq(su(1, 1)).- From "Quantum Groups" to "Quasi-Quantum Groups".- Symmetries of Icosahedral Quasicrystals.- Molecular Symmetry Adapted Bases in the Born-Oppenheimer Approximation.- On Certain Submodules of the Enveloping Fields.- Invariants and States Generating Symmetry of Nonstationary Systems.- Origins of Nuclear and Hadron Symmetries.- Projection Operator Method and Q-Analog of Angular Momentum Theory.- Symmetry Breaking and Fractional Quantization of Quantum Systems.- New Phases of D ? 2 Current and Diffeomorphism Algebras in Particle Physics.- Algebra and Geometry in the Theory of Mixed States.- Group Structures and the Interacting Boson Approximation for Nuclei.- Paradigms of Quantum Algebras.

The Symposium "Symmetries in Science V: Algebraic Systems: their Represen tations, Realizations and Physical Applications" was held at the Landesbildungszen trum Schloss Hofen, Vorarlberg, Austria, during the period July 30 - August 3, 1990. Leading scientists presented summaries, as well as recent research developments, con cerning their own field of specialization to the assembled international group of re searchers. These review-oriented presentations are included in this volume in order to make them available to the general scientific community. As was the case for the preceding Symposia we need to thank those who made Symposium V possible through their continued and generous support. These include, on part of the State of Vorarlbergj Dr. Martin Purtscher, Landeshauptmann Dr. Guntram Lins, Landesrat Ms. Elisabeth Gehrer, Landesratin and on part of Southern Illinois University at Carbondale; Dr. John C. Guyon, President Dr. Benjamin A. Shepherd, Vice President for Academic Affairs and Research Dr. John H. Yopp, Dean of the Graduate School Dr. Charles B. Klasek, Executive Assistant to the President for International and Economic Development Dr. Russell R. Dutcher, Dean of the College of Science Dr. Victoria J. Molfese, Director, Office of Research Development and Administration Dr. James D. Quisenberry, Acting Director of International Programs and Services Dr. Frank C. Sanders, Chairman of the Department of Physics. Finally, we need to especially thank Dr.