# Symmetry, Representations, and Invariants

Part of the Graduate Texts in Mathematics book series (GTM, volume 255)

Part of the Graduate Texts in Mathematics book series (GTM, volume 255)

Symmetry is a key ingredient in many mathematical, physical, and biological theories. Using representation theory and invariant theory to analyze the symmetries that arise from group actions, and with strong emphasis on the geometry and basic theory of Lie groups and Lie algebras, *Symmetry, Representations, and Invariants* is a significant reworking of an earlier highly-acclaimed work by the authors. The result is a comprehensive introduction to Lie theory, representation theory, invariant theory, and algebraic groups, in a new presentation that is more accessible to students and includes a broader range of applications.

The philosophy of the earlier book is retained, i.e., presenting the principal theorems of representation theory for the classical matrix groups as motivation for the general theory of reductive groups. The wealth of examples and discussion prepares the reader for the complete arguments now given in the general case.

Key Features of *Symmetry, Representations, and Invariants*:

• Early chapters suitable for honors undergraduate or beginning graduate courses, requiring only linear algebra, basic abstract algebra, and advanced calculus

• Applications to geometry (curvature tensors), topology (Jones polynomial via symmetry), and combinatorics (symmetric group and Young tableaux)

• Self-contained chapters, appendices, comprehensive bibliography

• More than 350 exercises (most with detailed hints for solutions) further explore main concepts

• Serves as an excellent main text for a one-year course in Lie group theory

• Benefits physicists as well as mathematicians as a reference work

Abstract algebra Group theory Matrix Multilinear Algebra Representation theory algebra linear algebra

- DOI https://doi.org/10.1007/978-0-387-79852-3
- Copyright Information Springer-Verlag New York 2009
- Publisher Name Springer, New York, NY
- eBook Packages Mathematics and Statistics
- Print ISBN 978-0-387-79851-6
- Online ISBN 978-0-387-79852-3
- Series Print ISSN 0072-5285
- About this book