Lie Theory and Its Applications in Physics II

The Table of Contents for the book is as follows:

• Preface
• I. Representation Theory
• I.A. Functional-Analytic Methods
  • Hardy Spaces in an Infinite Dimensional Setting
  • Non-Commutative Hardy Spaces and Toeplitz-Berezin Quantization
  • Reproducing Kernels on Vector Bundles
  • Unitary Representations with Reflection Symmetry
  • Séparation des Représentations Unitaires Irréductibles des Groupes de Lie Nilpotents
  • Class Operators as Intertwining Maps into the Group Algebra
• I.B. Lie-Algebraic Constructions
  • On Gradings of Lie Algebras and Representations
  • On Fine Gradings of Real Forms of sl(n, C)
  • Invariant Operators and Semi-Holonomic Verma Modules
  • Lie Algebra of Spherical Tensor Operators
• II. Applications to Physical Systems
• II.A. Quantum Systems
  • Review of Seiberg-Witten Model
  • Quantum Integrable Systems and Zonal Spherical Functions
  • On a Covariant Formulation of Quantum Mechanics
  • Torsion, Current Algebra, and Hamiltonian Quantization
  • Weak and Strong Separation Properties in Hierarchies of Nonlinear Quantum Time-Evolutions
  • Lie Super-Algebraisation of BRST-BFV Covariant Quantization
  • Algebra of Observables for QED on a Finite Lattice
  • On Interbasis Expansion for Isotropic Oscillator on Two-Dimensional Sphere
• II.B. Special Models
  • Infinite Quasi-Exactly Solvable Models
  • A Geometric Construction of Solutions of the DKP-Hierarchy
  • Explicit Calculations of Solutions of Heat Equations on Some Lie Groups
  • Lie Symmetry and Integrability of Ordinary Differential Equations by Quadratures
  • Gauge Field Theories in Terms of Graded Differential Lie Algebras
• III. Quantum Groups and Related Objects
  • Drinfeldians
  • Representations of the Quantum Algebra U_h(A_∞)
  • Quantum Homogeneous Vector Bundles and Representations of Quantum Groups
  • Elementary Representations and Intertwining Operators for Quantum Groups
  • Frame, Cotangent and Tangent Bundles of the Quantum Plane
• List of Participants