The Symposium ·Symmetries in Science VI: From the Rotation Group to Quantum Algebras· was held at the Cloister Mehrerau, Bregenz, Austria, during the period August 2-7, 1992. The Symposium was held in honor of Professor Lawrence C. Biedenharn on the occasion of his 70th birthday. During the academic year 1966/67 I worked as research associate with Larry at Duke University and we have ever since maintained close contact. It was thus natural for me to take the initiative and to organize this Symposium in honor of Larry as a great scientist and friend. The response which the Symposium received showed the favorable reaction by the scientific community to the opportunity provided by the Symposium to honor our colleague, teacher and friend. Equally, the scientific contributions contained in this volume illustrate the high esteem in which he is held. I wish to thank all the scientists who participated in the Symposium and who contributed to this volume. It is due to their commitment that the Symposium was successful. Finally I need to thank those who provided financial and logistical assistance to the Symposium: Dr. John H. Guyon, President of Southern Illinois University at Carbondale, Dr. Russell R. Dutcher, Dean, College of Science at SIUC, Dr. Maurice A. Wright, Chairman, Department of Physics, SIUC, Dr. Victoria J. Molfese, Office of Research Developement and Administration, SIUC, as well as Dr. Martin Purtscher, Landeshauptmann, Land Vorarlberg Dr. Guntram Lins, Landesrat, Land Vorarlberg.

The Symposium "Symmetries in Science VII: Spectrum Generating Algebras and Dynamic Symmetries in Physics" was held at the Southern Illinois University at Carbondale in Niigata, Japan Campus, during the period August 28-31, 1992. The Symposium was held in honor of Professor Francesco lachello on the occasion of his 50th birthday. We wish to thank the colleagues and friends of Franco for their participation in the Symposium as well as for contributing articles to this volume honoring him. It was their commitment and involvement which made this Symposium a success. We also wish to thank Dr. Jared H. Dorn, the director of SIUC-N, for his support in the planning and the execution of the Symposium. Moreover we wish to thank Mayor Nobuo Kumakura of Nakajo town and Mr. Kaichi Suzuki of the school entity "The Pacific" for their friendly support. Bruno Gruber, SIUC-N Takaharu Otsuka, University of Tokyo v LAUDATIO ON THE OCCASION OF THE 50TH BIRTHDAY OF PROFESSOR FRANCESCO IACHELLO I first met Franco lachello in 1974. Driving a smart Alfa-Romeo, he came to meet me at the station at Groningen where I was to spend a summer conducting research.

Thf3 symposium "Symmetries in Science VIII" was held in August of 1994 at the Cloister Mehrerau in Bregenz, Austria. The symposium was supported by Southern Illinois University at Carbondale, the Land Vorarlberg, and the Landeshaupstaot Bregenz. I wish to thank Dr. John C. Guyon, President of Southern Illinois University at Carbondale; Dr. Hubert Regner, Amt der Vorarlberger Landesregierung; and Dipl. Vw. Siegfried Gasser, Buergermeister der Landeshauptstadt Bregenz and Lantagsabgeordneter, for their generous support of the symposium. Finally I wish to thank Frater Albin of the Cloister Mehrerau for his support and cooperation in this endeavor, which made for a successful meeting in a most pleasant environment. Bruno Gruber v CONTENTS On Om x Gin Highest Weight Vectors Helmer Aslaksen, Eng-Chye Tan, and Chen-bo Zhu ... . Invariant Theory of Matrices Helmer Aslaksen, Eng-Chye Tan, and Chen-bo Zhu ... . 1 3 Symmetries of Elementary Particles Revisited A.O. Barut ... ... ... 21 Perturbative SU(1,1) Haluk Seker ... . ..., . ... 25 A Dual Structure for the Quantal Rotation Group, SU(2) L.C. Biedenharn and M.A. Lohe ..., . ... ... 37 Some Points in the Quantization of Relativistic Grassmann Dependent Interaction Systems A. Del Sol Mesa and R, P. Martinez y Romero ..., . ... 49 for Uq(sl(4)) and q-Conformal q-Difference Intertwining Operators I nvariant Equations V.K. Dobrev ... ... ... 55 A Quantum Mechanical Evolution Equation for Mixed States from Symmetry and Kinematics H.-D. Doebner and J.D. Hennig ... ... 85 vii Quantum Mechanical Motions over the Group Manifolds and Related Potentials I.H. Duru -. ... ... ...

Proceedings an International Symposium held in Bregenz, Austria, July 13-18, 1997

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

With applications in quantum field theory, general relativity and elementary particle physics, this three-volume work studies the invariance of differential operators under Lie algebras, quantum groups and superalgebras. This second volume covers quantum groups in their two main manifestations: quantum algebras and matrix quantum groups. The exposition covers both the general aspects of these and a great variety of concrete explicitly presented examples. The invariant q-difference operators are introduced mainly using representations of quantum algebras on their dual matrix quantum groups as carrier spaces. This is the first book that covers the title matter applied to quantum groups. Contents Quantum Groups and Quantum Algebras Highest-Weight Modules over Quantum Algebras Positive-Energy Representations of Noncompact Quantum Algebras Duality for Quantum Groups Invariant q-Difference Operators Invariant q-Difference Operators Related to GLq(n) q-Maxwell Equations Hierarchies

This is the first book to provide comprehensive treatment of the use of the symmetric group in quantum chemical structures of atoms, molecules, and solids. It begins with the conventional Slater determinant approach and proceeds to the basics of the symmetric group and the construction of spin eigenfunctions. The heart of the book is in the chapter dealing with spin-free quantum chemistry showing the great interpretation value of this method. The last three chapters include the unitary group approach, the symmetric group approach, and the spin-coupled valence bond method. An extensive bibliography concludes the book.

Candid Science VI concludes the series by narrating the conversations with famous scientists from the biomedical sciences, chemistry, and physics. There are 31 Nobel laureates and 11 other luminaries among them. The scientists are in the field of biomedical sciences, chemistry and physics.

This volume reviews some selected problems in solid state physics with an emphasis on adequate mathematical tools. The three main subjects are magnetic structures and neutron scattering; Berry phases and energy bands in solids (symmetry, analicity, Hofstadter butterfly, van Hove singularities); and quasicrystals, finite systems, and group action on sets (unitary group approach, Schur functions). Software presentations are included as a separate part.

The goal of the 2019 conference on Stochastic Processes and Algebraic Structures held in SPAS2019, Västerås, Sweden, from September 30th to October 2nd 2019 was to showcase the frontiers of research in several important topics of mathematics, mathematical statistics, and its applications. The conference has been organized along the following tracks: 1. Stochastic processes and modern statistical methods in theory and practice, 2. Engineering Mathematics, 3. Algebraic Structures and applications. This book highlights the latest advances in algebraic structures and applications focused on mathematical notions, methods, structures, concepts, problems, algorithms, and computational methods for the natural sciences, engineering, and modern technology. In particular, the book features mathematical methods and models from non-commutative and non-associative algebras and rings associated to generalizations of differential calculus, quantum deformations of algebras, Lie algebras, Lie superalgebras, color Lie algebras, Hom-algebras and their n-ary generalizations, semi-groups and group algebras, non-commutative and non-associative algebras and computational algebra interplay with q-special functions and q-analysis, topology, dynamical systems, representation theory, operator theory and functional analysis, applications of algebraic structures in coding theory, information analysis, geometry and probability theory. The book gathers selected, high-quality contributed chapters from several large research communities working on modern algebraic structures and their applications. The chapters cover both theory and applications, and are illustrated with a wealth of ideas, theorems, notions, proofs, examples, open problems, and results on the interplay of algebraic structures with other parts of Mathematics. The applications help readers grasp the material, and encourage them to develop new mathematical methods and concepts in their future research. Presenting new methods and results, reviews of cutting-edge research, open problems, and directions for future research, will serve as a source of inspiration for a broad range of researchers and students.