Representation Theory and Noncommutative Harmonic Analysis I: Fundamental Concepts. Representations of Virasoro and Affine Algebras

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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.