代换分析 |
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2020-06-21 00:00:00 |
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代换分析 内容简介
本书为D·E·卢瑟福的经典著作, 讲述了对称群的初步观点, 主要有导数的计算、杨氏公式、基偶数导数, 表的计算、正交和自然表示法、不变量二次方程、矩阵、群的特性、代换方程等内容。
代换分析 目录
Chapter Ⅰ THE CALCUIUS OF PERMUTATIONS 1 Permutations 2 The Symmetric Group fn 3 Cycles and Transpositions 4 Odd and Even Permutations 5 Classes of Permutations 7 The Positive and Negative Symmetric Groups on r Letters
Chapter Ⅱ THE CALCULUS OF TABIEAUX 1 Shapes and Tableaux 2 The Substitutional Expressions P and N 3 The Product PrNs 4 The Expressions E 5 von Neumann's Theorem 6 Young's Formula 7 Tableaux of Different Shapes
Chapter Ⅲ THE SEMI-NORMAL REPRESENTATION 1 Standard Tableaux 2 The Evaluation of fa 3 The Semi-normal Units e 4 Certain Fundamental Formulae 5 The Irreducible Semi-normal Representations of fn 6 Expressions which do not Involve the Last Letter 7 The Semi-normal Matrix for E 8 The Matrices U 9 The Matrices U
Chapter Ⅳ THE ORTHOGONAL AND NATURAL REPRESENTATIONS 1 Equivalent Representations 2 The Invariant Quadratic 3 The Tableau Function 4 The Orthogonal Representation 5 The Matrix 6 The Natural Representation 7 Expressions for the Units g 8 Equivalence of the Natural and Semi-normal Representations
Chapter Ⅴ GROUP CHARACTERS 1 The Expressions Cα 2 The Expressions Tα 3 The Relations between the Expressions Tκ and Cκ 4 The Group Characters of fn 5 The Evaluation of the Group Characters 6 Reduction Formulae 7 Littlewood's Theorem
Chapter Ⅵ SUBSTITUTIONAL EQUATIONS 1 Minimum Functions 2 The Master Idempotent 3 The Substitutional Properties of Functions 4 The Number of Independent Solutions of LX = 0 5 The Solution of the Equation LX = 0 6 Functions which are Invariant under a Group of Substitutional Expressions 7 Some Special Cases 8 The Equation LX = R Appendix TABLES FOR THE CASE n = 3 Bibliography Index
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