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Author James, G. D. (Gordon Douglas), 1945-
Title The representation theory of the symmetric group / Gordon James, Adalbert Kerber ; foreword by P.M. Cohn ; introduction by G. de B. Robinson.
Imprint Cambridge [Cambridgeshire] ; New York, NY, USA : Cambridge University Press, 1984.

Author James, G. D. (Gordon Douglas), 1945-
Series Encyclopedia of mathematics and its applications ; volume 16. Section, Algebra
Encyclopedia of mathematics and its applications ; v. 16.
Encyclopedia of mathematics and its applications. Section, Algebra.
Subject Symmetry groups.
Representations of groups.
Alt Name Kerber, Adalbert.
Description 1 online resource (xxviii, 510 pages) : illustrations.
polychrome rdacc
Note Imprint and ISBN from label on title page verso. Imprint on title page: Reading, Mass. : Addison-Wesley Pub. Co., Advanced Book Program, 1981.
Publication taken over by Cambridge University Press in 1984 with a new copyright date.
Bibliography Note Includes bibliographical references (pages 468-505) and index.
Note Print version record.
Summary 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.
Contents 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
ISBN 9781461944874 (electronic bk.)
1461944872 (electronic bk.)
9781107340732 (electronic bk.)
110734073X (electronic bk.)
0521302366
9780521302364
OCLC # 859537348
Additional Format Print version: James, G.D. (Gordon Douglas), 1945- Representation theory of the symmetric group 0521302366 (DLC) 85121560 (OCoLC)12371039


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