Contents -- Foreword -- Preface -- 1 A Conceptual Review of the New Approach to Group Representation Theory -- 1. Introduction -- 2. Three Kinds of Complete Set of Commuting Operators -- 3. The Relations between Permutation Group and Unitary Group -- 4. Postscript -- References -- 2 The Interacting Boson Model -- 1. Landmarks -- 2. Symmetries -- 3. Bridges -- 4. Avenues -- References -- 3 Structure of Nuclei Near the First Order Spherical- Deformed Phase Transition in the Interacting Boson Model -- 1. Introduction -- 2. Nature of Structural Evolution in the IBA -- 3. The Evolution of Nuclear Observables -- 4. Conclusion -- References -- 4 Dynamical Symmetry Approach to Collective Motions in Many-Body Systems -- 1. Introduction -- 2. The Dynamical Symmetry Approach -- 3. The Fermion Dynamical Symmetry Model -- 4. The SU(4) Model for High-Tc Superconductivity -- 5. The Energy Gap and Phase Diagrams in Cuprates -- 6. Summary -- References -- 5 Fermion Dynamical Symmetries and High Temperature Superconductors -- 1. Introduction -- 2. Fermion Dynamical Symmetries -- 3. The Dynamical Symmetry Method -- 4. An SU(4) Model of Superconductivity -- 5. SU(4) Model Hamiltonian -- 6. Dynamical Symmetry Chains -- 7. Coherent State Energy Surfaces -- 8. Phase Diagram -- 10. Relationship of SU(4) and Zhang's SO(5) -- 11. Analogies in Nuclear Structure -- 12. Summary -- References -- 6 The Nucleon-Pair Shell Model Truncated to the SD Subspace for Even-Even Nuclei -- 1. Introduction -- 2. The NPSM truncated to the SD subspace -- 3. The effect of the SD pair structure on the collectivity of low-lying states -- 4. Systematic study for Xe and Ba Isotopes -- 5. Neutron-Proton Tamm-Dancoff method in the NPSM -- 6. Summary -- References -- 7 Quantum Mechanics on a Sphere -- 1. Introduction -- 2. Motivation.

3. N-Particle States on the Sphere -- 4. Two-Particle States on the Sphere -- 5. Three Particle States on the Sphere -- 6. Summary -- References -- 8 The Method of Symmetrized Bosons -- 1. Introduction -- 2. Construction of the symmetry adapted basis -- 3. Diagonalization of the Hamiltonian -- 4. Intensities of infrared transitions -- 5. Intensities of Raman transitions -- 6. Outlook -- 7. Conclusions -- References -- 9 The Perturbed Dirac-Coulomb Problem via SO(2 l) Algebra. A Dilemma! -- 1. The Perturbed Dirac-Coulomb Problem. -- 2. Uniform Magnetic Field Perturbation. -- 3. Charmonium Confining Potential V(1) = Ar. -- 4. Harmonium Confining Potential V(1)(r) = Ar2. -- 5. Standard Perturbation Theory for the Dirac Hydrogen Atom Ground State -- References -- 10 Continuous Groups and Molecular Electronic Structure -- 1. Introduction -- 2. Spin Adaptation and UGA -- 3. Clifford Algebra UGA -- 4. Tensor Operator Algebra UGA -- 5. UGA/CAUGA and CC Methods -- 6. Spin-Dependent Operators -- 7. Conclusions -- References -- 11 The Irreducible Tensor Bases of Simple Lie Algebras -- 1. Introduction -- 2. Definitions and Notations -- 3. The Irreducible Tensor Bases of Classical Lie Algebras -- 4. The Irreducible Tensor Bases of Exceptional Lie Algebras -- 5. Conclusions -- References -- 12 Irreducible Bases in Icosahedral Group Space and Their Application -- 1. Introduction -- 2. Property of the icosahedral group I -- 3. Irreducible bases in group space of I -- 4. Applications -- 5. Conclusion -- References -- 13 Induction and Subduction Coefficients of Hecke and Coupling and Re-Coupling Coefficients of UQ(N) -- 1. Introduction -- 2. SDCs and IDCs of Hecke algebras -- 3. RCs and CGCs of quantum groups Uq(n) -- 4. Conclusions -- References -- 14 Algebraic Solutions for Point Groups -- 1. Introduction.

2. EFM and Its Application to Rotation Group -- 3. Point Group Symmetrized Boson Representation(SBR) -- 4. The Double-Induced Technique -- 5. The Group Chain O ] C4 -- 6. Conclusion -- References -- 15 Physical Method of Group Representation Theory. I. A New Approach to Theory of Finite-Group Representations -- 1. Introduction -- 2. Labelling of the Irreducible Representations and a Universal Method for the Calculation of Characters -- 3. Labelling and Determination of Irreducible Bases -- 4. Intrinsic Group -- 5. Decomposition of the Regular Representation and Calculation of Irreducible Matrix Elements -- 6. Calculation of Clebsch-Gordan Coefficients of Finite Groups -- References -- 16 Physical Method of Group Representation Theory. I. A New Approach to Theory of Finite-Group Representations (in Chinese) -- 17 Publications of Jin-Quan Chen.