The power of symmetries lies at the heart of interaction between modern mathematics and theoretical physics. A classic instance of such an interaction is the parallel development of Quantum Mechanics and that of the theory of finite dimensional representations of complex semi-simple lie algebras in the early 20th century. Natural questions arising from physics served as motivation for the development of the mathematical theory. The initiation of the theory of infinite dimensional representations of non-compact groups was also motivated by the need to understand the Representation Theory of the Poincare Group, the symmetry group of Special Relativity.Quantum Theory and Representation Theory have since flourished independently but have continued to benefit from a cross fertilization of ideas. In recent years, there has been renewed interest in this interaction centered especially around various Supersymmetric Quantum Field Theories and Geometric aspects of Representation Theory. These t...
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