典型群

內(nèi)容概要

　　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.

作者簡介

作者：（德國）韋爾（Hermann Weyl）

書籍目錄

TABLE OF CONTENTSPREFACE TO THE FIRST EDITIONPREFACE TO THE SECOND EDITIONCHAPTER IINTRODUCTION1. Fields, rings, ideals, polynomials2. Vector space3. Orthogonal transformations, Euclidean vector geometry4. Groups, Klein's Erlanger program..Quantities5. Invariants and covariantsCHAPTER IIVECTOR INVARIANTS1. Remembrance of things past2. The main propositions of the theory of invariantsA. Frost MAIN THEOREM3. First example: the symmetric group4. Capelli's identity5. Reduction of the first main problem by means of Capelli's identities6. Second example: the unimodular group ,.qL(n)7. Extension theorem. Third example: the group of step transformations8. A general method for including eontravariant arguments9. Fourth example: the orthogonal groupB. A CLOSE-UP OF THE ORTHOGONAL GROUP10. Cayley's rational parametrization of the orthogonal group11, Formal orthogonal invariants12. Arbitrary metric ground form13. The infinitesimal standpointC. THE SECOND MAIN THEOREM14. Statement of the proposition for the unimodular group15. Capelli's formal congruence16. Proof of the second main theorem for the unimodular group17. The second main theorem for the unimodular groupCHAPTER IIIMATRIC ALGEBRAS AND GROUP RINGSA. THEORY OF FULLY REDUCIBLE MATRIC ALGEBRAS1. Fundamental notions concerning matric algebras. The Schur lemma2. Preliminaries3. Representations of a simple algebra4. Wedderburn's theorem5. The fully reducible matric algebra and its commutator algebraB. THE RING OF A FINITE GROUP AND ITS COMMUTATOR ALGEBRA6. Stating the problem7. Full reducibility of the group ringTABLE  OF  CONTENTS8. Formal lemmas  .9. Reciprocity between group ring and commutator algebra10. A generalizationCHAPTER IVTHE SYMMETRIC GROUP AND THE FULL LINEAR GROUP1. Representation of a finite group in an algebraically closed field2. The Young symmetrizers. A combinatorial lsmma3. The irreducible representations of the symmetric group4. Decomposition of tensor space5. Quantities.  ExpansionCHAPTER VTHE ORTHOGONAL GROUPA. THE ENVELOPING ALGEBRA AND THE ORTHOGONAL IDEAL1. Vector invariants of the unimodular group again2. The enveloping algebra of the orthogonal group3. Giving the result its formal setting4. The orthogonal prime ideal5. An abstract algebra related to the orthogonal groupB. THE IRREDUCIBLE REPRESENTATIONS6. Decomposition by the trace operation7. The irreducible representations of the full orthogonal groupC. THE PROPER ORTHOGONAL GROUP8. Clifford's theorem9. Representations of the proper orthogonal groupCHAPTER VITHE SYMPLECTIC GROUP1. Vector invariants of the symplectic group2. Parametrization and unitary restriction3. Embedding algebra and representations of the symplectic groupCHAPTER VIICHARACTERS1. Preliminaries about unitary transformations2. Character for symmetrization or alternation alone3. Averaging over a group4. The volume element of the unitary group5. Computation of the characters6. The characters of GL(n).  Enumeration of covariants7. A purely algebraic approach8. Characters of the symplectic group9. Characters of the orthogonal group10. Decomposition and X-multiplication11. The Poinear~ polynomial……

章節(jié)摘錄

版權(quán)頁：插圖：

編輯推薦

《典型群(英文版)》是由世界圖書出版公司出版的。

圖書封面

圖書標簽Tags

無

評論、評分、閱讀與下載

---

    典型群 PDF格式下載

---