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Representations and Invariants of the Classical Groups

Representations and Invariants of the Classical Groups

Out of Print

Part of Encyclopedia of Mathematics and its Applications

  • Date Published: January 2000
  • availability: Unavailable - out of print December 2007
  • format: Paperback
  • isbn: 9780521663489

Out of Print

Unavailable - out of print December 2007
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About the Authors
  • More than half a century has passed since Weyl's "The Classical Groups" gave a unified picture of invariant theory that has retained its importance in mathematics and physics to the present day. This book presents an updated version of this theory together with many of the important recent developments. As a text for beginners, this book provides an introduction to the structure and finite-dimensional representation theory of the complex classical groups that requires only an abstract algebra course as a prerequisite. It makes abundant use of examples and exercises to explain concepts such as root systems, Weyl groups and highest weight theory. The more advanced reader will find an introduction to the structure and representations of complex reductive algebraic groups and their compact real forms. This book will also serve as a reference for the main results on tensor and polynomial invariants and the finite-dimensional representation theory of the classical groups. It will appeal to researchers in mathematics, statistics, physics and chemistry whose work involves symmetry groups, representation theory, invariant theory and algebraic group theory.

    • More difficult chapters arranged so results can be understood without reading details of proof
    • Self-contained, with appendices developing the basics of algebraic geometry, multilinear algebra, enveloping algebras of Lie algebras, manifolds and Lie groups
    • Over 300 exercises, most with hints for solution
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    Reviews & endorsements

    "In addition to providing a unified modern account of the subject, the authors often improve or complete the arguments found in the literature. With its wealth of concrete detail, the book can serve well as a reference work. The book is organized transparently and written with exceptional care." Mathematical Reviews

    "An enormous amount of care and intelligent work has obviously gone into the preparation of this text. The result is an incredibly rich...selection of beautiful topics from the current frontiers of representation theory and of invariant theory, whose study will be rewarding both to beginners and to experts in these fields." Bulletin of the American Mathematical Society

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    Product details

    • Date Published: January 2000
    • format: Paperback
    • isbn: 9780521663489
    • length: 703 pages
    • dimensions: 235 x 155 x 39 mm
    • weight: 0.98kg
    • contains: 29 b/w illus.
    • availability: Unavailable - out of print December 2007
  • Table of Contents

    1. Classical groups as linear algebraic groups
    2. Basic structure of classical groups
    3. Algebras and representations
    4. Polynomials and tensor invariants
    5. Highest weight theory
    6. Spinors
    7. Cohomology and characters
    8. Branching laws
    9. Tensor representations of GL(V)
    10. Tensor represenations of O(V) and Sp(V)
    11. Algebraic groups and homogeneous spaces
    12. Representations on Aff(X)
    A. Algebraic geometry
    B. Linear and multilinear algebra
    C. Associative algebras and Lie algebras
    D. Manifolds and Lie groups.

  • Authors

    Roe Goodman, Rutgers University, New Jersey

    Nolan R. Wallach, University of California, San Diego

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