Representation Theory of Semisimple Groups: An Overview Based on Examples

Description

In this classic work, Anthony W. Knapp offers a survey of representation theory of semisimple Lie groups in a way that reflects the spirit of the subject and corresponds to the natural learning process. This book is a model of exposition and an invaluable resource for both graduate students and researchers. Although theorems are always stated precisely, many illustrative examples or classes of examples are given. To support this unique approach, the author includes for the reader a useful 300-item bibliography and an extensive section of notes. Title Contents Preface to the Princeton Landmarks in Mathematics Edition Preface I. Scope of the Theory II. Representations of SU(2), SL(2, R) and SL(2, C) III. Cinfty Vectors and the Universal Enveloping Algebra IV. Representations of Compact Lie Groups V. Structure Theory for Noncompact Groups VI. Holomorphic Discrete Series VII. Induced Representations VIII. Admissible Representations IX. Construction of Discrete Series X. Global Characters XI. Introduction to Plancherel Formula XII. Exhaustion of Discrete Series XIII. Plancherel Formula XIV. Irreducible Tempered Representations XV. Minimal K Types XVI. Unitary Representations Appendix A. Elementary Theory of Lie Groups Appendix B. Regular Singular Points of Partial Differential Equations Appendix C. Roots and Restricted Roots for Classical Groups Notes References Index of Notation Index