## The Classical Groups: Their Invariants and Representations, Issue 1, Part 1In 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. |

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### Contents

III | 1 |

IV | 6 |

V | 11 |

VI | 13 |

VII | 23 |

VIII | 27 |

IX | 29 |

X | 36 |

XLIX | 169 |

L | 173 |

LI | 176 |

LII | 181 |

LIII | 185 |

LIV | 194 |

LV | 198 |

LVI | 201 |

XI | 39 |

XII | 42 |

XIII | 45 |

XIV | 47 |

XV | 49 |

XVI | 52 |

XVII | 56 |

XVIII | 62 |

XIX | 65 |

XX | 66 |

XXI | 70 |

XXII | 72 |

XXIII | 75 |

XXIV | 79 |

XXV | 84 |

XXVI | 87 |

XXVII | 90 |

XXVIII | 93 |

XXIX | 96 |

XXX | 101 |

XXXI | 106 |

XXXII | 107 |

XXXIII | 112 |

XXXIV | 115 |

XXXV | 119 |

XXXVI | 124 |

XXXVII | 127 |

XXXVIII | 131 |

XXXIX | 137 |

XL | 140 |

XLI | 143 |

XLII | 144 |

XLIII | 147 |

XLIV | 149 |

XLV | 153 |

XLVI | 159 |

XLVII | 163 |

XLVIII | 165 |

LVII | 208 |

LVIII | 216 |

LIX | 222 |

LX | 229 |

LXI | 232 |

LXII | 239 |

LXIII | 243 |

LXIV | 246 |

LXV | 248 |

LXVI | 250 |

LXVII | 251 |

LXVIII | 252 |

LXIX | 254 |

LXX | 258 |

LXXI | 262 |

LXXII | 265 |

LXXIII | 268 |

LXXIV | 270 |

LXXV | 274 |

LXXVI | 275 |

LXXVII | 276 |

LXXVIII | 280 |

LXXIX | 283 |

LXXX | 286 |

LXXXI | 288 |

LXXXII | 291 |

LXXXIII | 293 |

LXXXIV | 294 |

LXXXV | 295 |

LXXXVI | 296 |

LXXXVII | 299 |

LXXXVIII | 300 |

LXXXIX | 303 |

XC | 307 |

308 | |

314 | |

317 | |

### Other editions - View all

The Classical Groups: Their Invariants and Representations (PMS-1) Hermann Weyl Limited preview - 2016 |

The Classical Groups: Their Invariants and Representations, Issue 1, Part 1 Hermann Weyl Limited preview - 1946 |