对称群 : 第2版

preface to the 2nd edition

preface to the 1st eition

1 group representations

1.1 fundamental concepts

1.2 matrix representations

1.3 g-modules and the group algebra

1.4 reducibility

1.5 complete reducibility and maschke's theorem

1.6 g-homomorphisms and schur's lemma

1.7 commutant and endomorphism algebras

1.8 group characters

1.9 inner products of characters

1.10 decomposition of the group algebra

1.11 tensor products again

1.12 restricted and induced representations

1.13 exercises

2 representations of the symmetric group

2.1 young subgroups, tableaux, and tabloids

2.2 dominance and lexicographic ordering

2.3 specht modules

2.4 the submodule theorem

2.5 standard tableaux and a basis for s

2.6 garnir elements

2.7 young's natural representation

2.8 the branching rule

2.9 the decomposition of my

2.10 the semistandard basis for hom（s, m）

2.11 kostka numbers and young's rule

2.12 exercises

3 combinatorial algorithms

3.1 the robinson-schensted algorithm

3.2 column insertion

3.3 increasing and decreasing subsequences

3.4 the knuth relations

3.5 subsequences again

3.6 viennot's geometric construction

3.7 schutzenberger's jeu de taquin

3.8 dual equivalence

3.9 evacuation

3.10 the hook formula

3.11 the determinantal formula

3.12 exercises

4 symmetric functions

4.1 introduction to generating functions

4.2 the hillman-grassl algorithm

4.3 the ring of symmetric functions

4.4 schur functions

4.5 the jacobi-trudi determinants

4.6 other definitions of the schur function

4.7 the characteristic map

4.8 knuth's algorithm

4.9 the littlewood-richardson rule

4.10 the murnnghan-nakayama rule

4.11 exercises

5 applications and generalizations

5.1 young's lattice and differential posets

5.2 growths and local rules

5.3 groups acting on posets

5.4 unimodality

5.5 chromatic symmetric functions

5.6 exercises

bibliography

index

《对称群（第2版）》是一部研究生教程，几乎囊括了该领域的重要结果，是经典中的经典。书中包括了很多新资料，例如，hook公式的novelli-pak-stoyanovskii证明，运用偏微分部分有序集的平方和证明，平方和公式的fomin双射证明，部分有序集上的群行为及其在单峰性证明中应用和色对称函数。