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.

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.