典型群（簡體書）

《典型群(英文版)》內容簡介：Ever since the year 1925, when I succeeded in determining the characters of the semi-simple continuous groups by a combination of E. Cartans infini-tesimal methods and I. Schurs integral procedure, I have looked toward thegoal of deriving the decisive results for the most important of these groups bydirect algebraic construction, in particular for the full group of all non-singu-lar linear transformations and for the orthogonal group. Owing mainly toR. Brauers intervention and collaboration during the last few years, it nowappears that I have in my hands all the tools necessary for this purpose. Thetask may be characterized precisely as follows: with respect to the assignedgroup of linear transformations in the underlying vector space, to decomposethe space of tensors of given rank into its irreducible invariant subspaces.

作者：（德國）韋爾（Hermann Weyl）

TABLE OF CONTENTS
PREFACE TO THE FIRST EDITION
PREFACE TO THE SECOND EDITION
CHAPTER I
INTRODUCTION
1. Fields, rings, ideals, polynomials
2. Vector space
3. Orthogonal transformations, Euclidean vector geometry
4. Groups, Kleins Erlanger program..Quantities
5. Invariants and covariants
CHAPTER II
VECTOR INVARIANTS
1. Remembrance of things past
2. The main propositions of the theory of invariants
A. Frost MAIN THEOREM
3. First example: the symmetric group
4. Capellis identity
5. Reduction of the first main problem by means of Capellis identities
6. Second example: the unimodular group ,.qL(n)
7. Extension theorem. Third example: the group of step transformations
8. A general method for including eontravariant arguments
9. Fourth example: the orthogonal group
B. A CLOSE-UP OF THE ORTHOGONAL GROUP
10. Cayleys rational parametrization of the orthogonal group
11, Formal orthogonal invariants
12. Arbitrary metric ground form
13. The infinitesimal standpoint
C. THE SECOND MAIN THEOREM
14. Statement of the proposition for the unimodular group
15. Capellis formal congruence
16. Proof of the second main theorem for the unimodular group
17. The second main theorem for the unimodular group
CHAPTER III
MATRIC ALGEBRAS AND GROUP RINGS
A. THEORY OF FULLY REDUCIBLE MATRIC ALGEBRAS
1. Fundamental notions concerning matric algebras. The Schur lemma
2. Preliminaries
3. Representations of a simple algebra
4. Wedderburns theorem
5. The fully reducible matric algebra and its commutator algebra
B. THE RING OF A FINITE GROUP AND ITS COMMUTATOR ALGEBRA
6. Stating the problem
7. Full reducibility of the group ring
TABLE OF CONTENTS
8. Formal lemmas .
9. Reciprocity between group ring and commutator algebra
10. A generalization
CHAPTER IV
THE SYMMETRIC GROUP AND THE FULL LINEAR GROUP
1. Representation of a finite group in an algebraically closed field
2. The Young symmetrizers. A combinatorial lsmma
3. The irreducible representations of the symmetric group
4. Decomposition of tensor space
5. Quantities. Expansion
CHAPTER V
THE ORTHOGONAL GROUP
A. THE ENVELOPING ALGEBRA AND THE ORTHOGONAL IDEAL
1. Vector invariants of the unimodular group again
2. The enveloping algebra of the orthogonal group
3. Giving the result its formal setting
4. The orthogonal prime ideal
5. An abstract algebra related to the orthogonal group
B. THE IRREDUCIBLE REPRESENTATIONS
6. Decomposition by the trace operation
7. The irreducible representations of the full orthogonal group
C. THE PROPER ORTHOGONAL GROUP
8. Cliffords theorem
9. Representations of the proper orthogonal group
CHAPTER VI
THE SYMPLECTIC GROUP
1. Vector invariants of the symplectic group
2. Parametrization and unitary restriction
3. Embedding algebra and representations of the symplectic group
CHAPTER VII
CHARACTERS
1. Preliminaries about unitary transformations
2. Character for symmetrization or alternation alone
3. Averaging over a group
4. The volume element of the unitary group
5. Computation of the characters
6. The characters of GL(n). Enumeration of covariants
7. A purely algebraic approach
8. Characters of the symplectic group
9. Characters of the orthogonal group
10. Decomposition and X-multiplication
11. The Poinear~ polynomial
……