The Classical Groups: Their Invariants and Representations

Contents: 1.Introduction 2. Vector Invariants 3. Matric Algebras and Group Rings 4. The Symmetric Group and the Full Linear Group 5. The Orthogonal Group 6. The Symplectic Group 7. Characters 8. General Theory of Invariants 9. Matric Algebras Resumed. Supplements. Errata and Addenda Bibliography. Supplementary Bibliography. Index

In this renowned volume, Hermann Weyl discusses the symmetric, full linear, orthogonal, and symplectic groups and determines their different invariants and representations. Using basic concepts from algebra, he examines the various properties of the groups. Analysis and topology are used wherever appropriate. The book also covers topics such as matrix algebras, semigroups, commutators, and spinors, which are of great importance in understanding the group-theoretic structure of quantum mechanics.