Symmetries in Science VI: From the Rotation Group to Quantum Algebras

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.

Table of Contents:
Deformable Media with Microstructure.- Biorthogonal and Orthogonal Bases in the Missing Label Problem.- Lie Ideals and Symmetric Bi-Derivations of Prime Rings.- From Q-Oscillators to Quantum Groups.- An Analog of the Fourier Transformation for a q-Harmonic Oscillator.- Geometry, Group Theory and Partitions.- Origin of Spin: From Rotation Group to Noncommutative Zitterbewegung.- Massless Representations of the Poincaré Group and Conformai Invariance.- q-Deformed Oscillators in Nuclear and Molecular Physics.- Induced Representations and the Frobenius Theorem for Finite Quantum Groups.- Non-Abelian Surprises for Gauge Fields Coupled to Gravity.- Colored Supersymmetry of Mesons and Baryons based on Octonionic Algebras.- Quantum Algebras and Lie Groups.- q-Fock Space Representations of the q-Lorentz Algebra and Irreducible Tensors.- Construction of Quantum Groups and the Yang-Baxter Equation with Spectral Parameter.- Supersymmetry and the Nonlocal Yangian Deformation Symmetry.- Quantum Algebras: Representations and Real Forms.- Lagrangians from Equations: a Skyrmion Case Study.- Probability, Representations, and Coordinates on Lie Groups.- A Quantum Algebraic Interpretation of the Basic Hypergeometric Series r?s.- Generalized Lie Algebras.- Geometrization of Mechanics.- The Fractional Quantum Hall Effect and the Rotation Group.- Universal Regularities in Multiparticle Production.- On the Octonionic Nahm Equations and Self-Dual Membranes in 9 Dimensions.- Vector Coherent State Constructions of U(3) Canonical Shift Tensors of Biedenharn-Louck Type.- New Applications of the Biedenharn-Temple Operator.- On the Group Theory of the Polarization States of a Gauge Field.- Representation Theory of Finite Groups.- Fate of Classical Symmetry in Field Theory.- Quark Rotation Groupsfor the Atomic f Shell.- Z3-Grading and Ternary Algebraic Structures.- Infinite Dimensional Representations of Quantum Algebras.- Free Groups, their Automorphism Groups, Applications.- Upper Bound on the Top Quark Mass for Supersymmetric SU(5) Model.- Representations of Classical Groups on the Lattice and its Application to the Field Theory on Discrete Space-Time.- From the Rotation Group to the Poincaré Group.- D=4 Quantum Poincaré-Heisenberg Algebra.- ?-Deformed Poincaré Algebra and some Physical Consequences.- Geometrical Phase, Generalized Quasienergy and Floquet Operator as Invariants.- Algebraic Structure of Observables in Nonequilibrium Thermodynamics and their Biological Significance.- The Dirac Oscillator and a Baryon Mass Formula.- Universal SU(2/1) and the Higgs and Fermion Masses.- Novel Implications of the q-Analogue Coherent States.- Covariant Quantum Algebras.- Q-Deformation of Para-Fermi Commutation Relations.- Yang-Baxter Equation and the Triple Product Systems.- Spin-Statistics and Topology.- Unitary Group Approach to Valence Bond and Coupled Cluster Methods.- Is There Any Relation between N Pairs of Deformed Q-Bosons and Uq[OSP(1/2N)]?.- q-Bosons and Irreducible Tensors for q-Algebras.- Noncommutative Dynamics.- The Biedenharn-Louck Tensor Calculus from a Vector Coherent State Perspective.- QCD Originated Dynamical (Super) Symmetry for Hadrons.- The Two-Dimensional Symplectic and Metaplectic Groups and their Universal Cover.- Some Aspects of q-Boson Calculus.- Quantum Group Analogues of Squeezed States.- The Pauli Principle and Systems Consisting of Composite Particles.- Quantum Galilei Group as a Symmetry of the Heisenberg Linear Magnetic Chain.- Aspects of Lie Algebra Quantization.- Parallel Lifts and Holonomy along Density Operators:Computable Examples using O(3)-Orbits.- Covariant Form of Center of Energy.- Yet Another Form of the Relation Between Quantum and Classical Physics.