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Representations and Invariants of the Classical Groups

Representations and Invariants of the Classical Groups

Part of Encyclopedia of Mathematics and its Applications

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


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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. This book presents an updated version of this theory together with many of the important recent developments. As a text for those new to the area, 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. 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

    'It is no prophecy to state that this book will become an important reference work, but it will also serve as an excellent textbook for various courses.' G. Kowol, Book Reviews

    'This remarkable book is indeed an encyclopedic treatment of the classical groups and their representation theory … an excellent reference source … the book will be a very valuable item in each private or public library.' European Mathematical Society

    'With its wealth of material covered, this book will be the reference book on these topics for the next decades.' Ch. Krattenthaler, Internationale Mathematische Nachrichten

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    Product details

    • Date Published: March 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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