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.
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.
This book presents an updated version of Weyl's invariant theory of the classical groups, together with many of the important recent developments. An introductory and more advanced graduate level text, it is also a reference for researchers whose work involves symmetry groups, representation theory, invariant theory and algebraic group theory.
Presents an updated version of Weyl's invariant theory of the classical groups, together with many of the important recent developments.
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.
This book presents an updated version of Weyl's invariant theory of the classical groups, together with many of the important recent developments. An introductory and more advanced graduate level text, it is also a reference for researchers whose work involves symmetry groups, representation theory, invariant theory and algebraic group theory.
Presents an updated version of Weyl's invariant theory of the classical groups, together with many of the important recent developments.