Representation Theory of the Symmetric Group

Preface
Contents
I - THE ORDINARY AND THE MODULAR REPRESENTATION THEORY OF A FINITE GROUP
	Part 1 : The ordinary representation theory
		Introduction
		11.1 Permutation representations
		11.2 The group algebra over a field F
		11.3 Character theory
		11.4 Applications
		11.5 Induced representations
	Part 2 : The modular representation theory
		Introduction
		12.1 The decomposition matrix D
		12.2 Modular characters
		12.3 Indecomposable and modularly irreducible representations
		12.4. Character relations
		12.5 Blocks
		12.6 The Nakayama reciprocity formulae
II - ORDINARY REPRESENTATION THEORY OF Sn AND YOUNG'S RAISING OPERATOR
	Introduction
	2.1 Young's representation theory of S_n
	2.2 Young's raising operator R_{ik}
	2.3 The degree f^λ and the hook graph H[λ]
	2.4 Lattice permutations
	2.5 Skew diagrams
III - S_n AND THE FULL LINEAR GROUP GL(d)
	Introduction
	3.1 Inducing and restricting
	3.2 The irreducible representation of GL(d)
	3.3 The outer product [μ] . [v]
	3.4 The inner product [α] x [β]
	3.5 Symmetrized outer products [μ] \odot [v]
	3.6 Symmetrized inner products [μ] ⊗ [v]
IV - THE CHARACTERS OF S_n AND THE CONTENT OF [λ]
	Introduction
	4.1 Character of a cycle
	4.2 Characters of S_n
	4.3 The content of [λ]
	4.4 The q-hook structure of [λ]
	4.5 Character of a product of mq-cycles
	4.6 The translation operator T
V - THE p-BLOCK STRUCTURE OF S_n
	Introduction
	5.1 Construction of [λ] from [λ]_q and the q-core [\tilde{λ}]
	5.2 The hook graph H[λ]
	5.3 The blocks of S_n
	5.4 The primeness of q
VI - THE DIMENSIONS OF A p-BLOCK
	Introduction
	6.1 r-inducing and r-restricting
	6.2 The r-Boolean algebra associated with [λ]
	6.3 q-regular and q-singular Young diagrams
	6.4 p-regular diagrams and p-regular classes of S_n
	6.5 The number of modular irreducible representations in a block
VII - THE INDECOMPOSABLES OF S_n
	Introduction
	7.1 The D-matrix of a block of weight 1 of S_n
	7.2 The D-matrix of a block of weight 2 of S_{2p}
	7.3 Standard tableaux
	7.4 The raising operator
	7.5 Head and foot diagrams
	7.6 The Nakayama reciprocity formulae
VIII - THE MODULAR IRREDUCIBLE REPRESENTATIONS OF S_n
	Introduction
	8.1 Congruence properties
	8.2 The transforming matrix L
	8.3 The raising operator
	8.4 Decomposition matrices
	8.5 r-Boolean algebras
Notes and References
Bibliography
Appendix (Tables)
Index