Symmetry, Representations, and Invariants

• Main Authors: Goodman, Roe (Author), Wallach, Nolan R. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2009.
• Series: Graduate Texts in Mathematics, 255
• Subjects: Mathematics.; Algebra.; Group theory.; Topological groups.; Lie groups.; Geometry.; Physics.; Group Theory and Generalizations.; Mathematical Methods in Physics.; Topological Groups, Lie Groups.; General Algebraic Systems.

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, Represen...

Table of Contents:

• Lie Groups and Algebraic Groups
• Structure of Classical Groups
• Highest-Weight Theory
• Algebras and Representations
• Classical Invariant Theory
• Spinors
• Character Formulas
• Branching Laws
• Tensor Representations of GL(V)
• Tensor Representations of O(V) and Sp(V)
• Algebraic Groups and Homogeneous Spaces
• Representations on Spaces of Regular Functions.