Representation Theory And Noncommutative Harmonic Analysis I: Fundamental Concepts. Representations Of Virasoro And Affine Algebras (encyclopaedia Of Mathematical Sciences (22)) (v. 1)

Part I of this book is a short review of the classical part of representation theory. The main chapters of representation theory are discussed: representations of finite and compact groups, finite- and infinite-dimensional representations of Lie groups. It is a typical feature of this survey that the structure of the theory is carefully exposed - the reader can easily see the essence of the theory without being overwhelmed by details. The final chapter is devoted to the method of orbits for different types of groups. Part II deals with representation of Virasoro and Kac-Moody algebra. The second part of the book deals with representations of Virasoro and Kac-Moody algebra. The wealth of recent results on representations of infinite-dimensional groups is presented. This Two-part Survey Provides A Short Review Of The Classical Part Of Representation Theory, Carefully Exposing The Structure Of The Theory Without Overwhelming Readers With Details, And Deals With Representations Of Virasoro And Kac-moody Algebra. It Presents A Wealth Of Recent Results On Representations Of Infinite-dimensional Groups. Front Matter....Pages i-vii Introduction to the Theory of Representations and Noncommutative Harmonic Analysis....Pages 1-156 Representations of Virasoro and Affine Lie Algebras....Pages 157-225 Back Matter....Pages 227-236 An action of a topological group G on a topological space X is defined in the same way as above with the additional requirement that the maps in (2.1) and (2.1') be continuous. v. 1. Fundamental concepts, representations of Virasoro and affine algebras v. 2. Homogeneous spaces, representation and special functions.