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The representation theory of the symmetric group /
The Representation Theory of the Symmetric Group provides an account of both the ordinary and modular representation theory of the symmetric groups. The range of applications of this theory is vast, varying from theoretical physics, through combinatories to the study of polynomial identity algebras;...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge [Cambridgeshire] ; New York, NY, USA :
Cambridge University Press,
1984.
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| Colección: | Encyclopedia of mathematics and its applications ;
v. 16. Encyclopedia of mathematics and its applications. Section, Algebra. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Half Title; Series Page; Title; Copyright; Contents; Editor's Statement; Foreword; Introduction; References; Preface; List of Symbols; CHAPTER 1 Symmetric Groups and Their Young Subgroups; 1.1 Symmetric and Alternating Groups; 1.2 The Conjugacy Classes of Symmetric and Alternating Groups; 1.3 Young Subgroups of Sn and Their Double Cosets; 1.4 The Diagram Lattice; 1.5 Young Subgroups as Horizontal and Vertical Groups of Young Tableaux; Exercises; CHAPTER 2 Ordinary Irreducible Representations and Characters of Symmetric and Alternating Groups
- 2.1 The Ordinary Irreducible Representations of Sn2.2 The Permutation Characters Induced by Young Subgroups; 2.3 The Ordinary Irreducible Characters as Z-linear Combinations of Permutation Characters; 2.4 A Recursion Formula for the Irreducible Characters; 2.5 Ordinary Irreducible Representations and Characters of An; 2.6 Sn is Characterized by its Character Table; 2.7 Cores and Quotients of Partitions; 2.8 Young's Rule and the Littlewood-Richardson Rule; 2.9 Inner Tensor Products; Exercises; CHAPTER 3 Ordinary Irreducible Matrix Representations of Symmetric Groups
- 5.3 Permutrization of Representations5.4 Plethysms of Representations; 5.5 Multiply Transitive Groups; Exercises; CHAPTER 6 Modular Representations; 6.1 The p-block Structure of the Ordinary Irreducibles of Sn and An; Generalized Decomposition Numbers; 6.2 The Dimensions of a p-block; u-numbers; Defect Groups; 6.3 Techniques for Finding Decomposition Matrices; Exercises; CHAPTER 7 Representation Theory of Sn over an Arbitrary Field; 7.1 Specht Modules; 7.2 The Standard Basis of the Specht Module; 7.3 On the Role of Hook Lengths; Exercises; CHAPTER 8 Representations of General Linear Groups
- 8.1 Weyl Modules8.2 The Hyperalgebra; 8.3 Irreducible GL(m, F)-modules over F; 8.4 Further Connections between Specht and Weyl Modules; Exercises; APPENDIX I: Tables; I.A Character Tables; I.B Class Multiplication Coefficients; I.C Representing Matrices; I.D Decompositions of Symmetrizations and Permutrizations; I.E Decomposition Numbers; I.F Irreducible Brauer Characters; I.G Littlewood-Richardson Coefficients; I.H Character Tables of Wreath Products of Symmetric Groups; I.I Decompositions of Inner Tensor Products; APPENDIX II: Notes and References; II. A Books and Lecture Notes