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Home > Mathematics and Science Textbooks > Mathematics > Groups and group theory > Representations and Invariants of the Classical Groups: (Series Number 68 Encyclopedia of Mathematics and its Applications)
Representations and Invariants of the Classical Groups: (Series Number 68 Encyclopedia of Mathematics and its Applications)

Representations and Invariants of the Classical Groups: (Series Number 68 Encyclopedia of Mathematics and its Applications)


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About the Book

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.

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.

Review :
'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
  • ISBN-13: 9780521663489
  • Publisher: Cambridge University Press
  • Publisher Imprint: Cambridge University Press
  • Height: 235 mm
  • No of Pages: 703
  • Returnable: N
  • Returnable: N
  • Spine Width: 39 mm
  • Width: 155 mm
  • ISBN-10: 0521663482
  • Publisher Date: 13 Jan 2000
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Returnable: N
  • Series Title: Series Number 68 Encyclopedia of Mathematics and its Applications
  • Weight: 980 gr


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