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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Wallach, Nolan R. Harmonic analysis on homogeneous spaces. Mineola, New York : Dover Publications, Inc., 2018 (DLC) 2017058420 (OCoLC)1019835004 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Nolan R Wallach |

ISBN: | 9780486836430 0486836436 |

OCLC Number: | 1082193848 |

Notes: | "This Dover edition, first published in 2018, is a revised and corrected republication of the work originally published in 1973 by Marcel Dekker, Inc., New York, as part of the "Pure and Applied Mathematics" series"--Bibliographical note. |

Description: | 1 online resource (xxiii, 357 pages). |

Contents: | Vector bundles -- Elementary representation theory -- Basic structure theory of compact lie groups and semisimple lie algebras -- The topology and representation theory of compact lie groups -- Harmonic analysis on a homogeneous vector bundle -- Holomorphic vector bundles over flag manifolds -- Analysis on semisimple lie groups -- Representations of semisimple lie groups. |

Series Title: | Dover books on mathematics. |

Responsibility: | Nolan R. Wallach, University of California, San Diego. |

### Abstract:

This book is suitable for advanced undergraduate and graduate students in mathematics with a strong background in linear algebra and advanced calculus. Early chapters develop representation theory of compact Lie groups with applications to topology, geometry, and analysis, including the Peter-Weyl theorem, the theorem of the highest weight, the character theory, invariant differential operators on homogeneous vector bundles, and Bott's index theorem for such operators. Later chapters study the structure of representation theory and analysis of non-compact semi-simple Lie groups, including the principal series, intertwining operators, asymptotics of matrix coefficients, and an important special case of the Plancherel theorem. Teachers will find this volume useful as either a main text or a supplement to standard one-year courses in Lie groups and Lie algebras. The treatment advances from fairly simple topics to more complex subjects, and exercises appear at the end of each chapter. Eight helpful Appendixes develop aspects of differential geometry, Lie theory, and functional analysis employed in the main text.

Requiring background in linear algebra and advanced calculus, this text covers representation theory of compact Lie groups with applications to topology, geometry, and analysis and non-compact semi-simple Lie groups. 1973 edition.

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