UID:
almafu_9959237543302883
Format:
1 online resource (xxviii, 510 pages) :
,
digital, PDF file(s).
ISBN:
1-316-08679-8
,
0-521-10412-2
,
1-107-29884-9
,
1-107-47847-2
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1-107-34073-X
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1-107-47838-3
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1-107-47851-0
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1-107-47842-1
Series Statement:
Encyclopedia of mathematics and its applications ; volume 16
Content:
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; and new uses are still being found.
Note:
Title from publisher's bibliographic system (viewed on 10 Dec 2015).
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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
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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
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3.1 A Decomposition of the Group Algebra QSn into Minimal Left Ideals3.2 The Seminormal Basis of QSn; 3.3 The Representing Matrices; 3.4 The Orthogonal and the Natural Form of [α]; Exercises; CHAPTER 4 Representations of Wreath Products; 4.1 Wreath Products; 4.2 The Conjugacy Classes of GwrSn; 4.3 Representations of Wreath Products over Algebraically Closed Fields; 4.4 Special Cases and Properties of Representations of Wreath Products; Exercises; CHAPTER 5 Applications to Combinatorics and Representation Theory; 5.1 The Pοĺya Theory of Enumeration; 5.2 Symmetrization of Representations
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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
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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
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II.B Comments on the Chapters
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English
Additional Edition:
ISBN 1-306-07239-5
Additional Edition:
ISBN 0-521-30236-6
Language:
English
URL:
https://doi.org/10.1017/CBO9781107340732
