The Classical Groups: Their Invariants and Representations (PMS-1)Princeton University Press, 2 juin 2016 - 336 pages 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. |
Table des matières
1 | |
CHAPTER II VECTOR INVARIANTS | 27 |
CHAPTER III MATRIC ALGEBRAS AND GROUP RINGS | 79 |
CHAPTER IV THE SYMMETRIC GROUP AND THE FULL LINEAR GROUP | 115 |
CHAPTER V THE ORTHOGONAL GROUP | 137 |
CHAPTER VI THE SYMPLECTIC GROUP | 165 |
CHAPTER VII CHARACTERS | 176 |
CHAPTER VIII GENERAL THEORY OF INVARIANTS | 239 |
CHAPTER IX MATRIC ALGEBRAS RESUMED | 280 |
CHAPTER X SUPPLEMENTS | 291 |
ERRATA AND ADDENDA | 307 |
BIBLIOGRAPHY | 308 |
SUPPLEMENTARY BIBLIOGRAPHY MAINLY FOR THE YEARS 19401945 | 314 |
317 | |