The Representation Theory of the Symmetric Groups

Background from representation theory....Pages 1-4
The symmetric group....Pages 5-7
Diagrams, tableaux and tabloids....Pages 8-12
Specht modules....Pages 13-17
Examples....Pages 18-21
The character table of ....Pages 22-26
The garnir relations....Pages 27-28
The standard basis of the specht module....Pages 29-33
The branching theorem....Pages 34-35
p-regular partitions....Pages 36-38
The irreducible representations of ....Pages 39-41
Composition factors....Pages 42-43
Semistandard homomorphisms....Pages 44-50
Young’s rule....Pages 51-53
Sequences....Pages 54-59
The Littlewood-richardson rule....Pages 60-64
A specht series for M μ ....Pages 65-72
Hooks and skew-hooks....Pages 73-73
The determinantal form....Pages 74-76
The hook formula for dimensions....Pages 77-78
The murnaghan-nakayama rule....Pages 79-86
Binomial coefficients....Pages 87-88
Some irreducible specht modules....Pages 89-97
On the decomposition matrices of ....Pages 98-113
Young’s orthogonal form....Pages 114-124
Representations of the general linear group....Pages 125-135