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

自然科学 数学 代数数论组合理论

在线阅读