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. : AddisonWesley 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 468505) 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 Zlinear 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 LittlewoodRichardson 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 pblock Structure of the Ordinary Irreducibles of Sn and An; Generalized Decomposition Numbers; 6.2 The Dimensions of a pblock; unumbers; 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 LittlewoodRichardson 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 
