对称群（第2版）

图书标准信息

• 作者 Bruce E. Sagan 编
• 出版社 世界图书出版公司
• 出版时间 2012-06
• 版次 2
• ISBN 9787510044021
• 定价 45.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 238页
• 正文语种 英语

【内容简介】

《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。

【目录】

prefacetothe2ndedition
prefacetothe1steition
1grouprepresentations
1.1fundamentalconcepts
1.2matrixrepresentations
1.3g-modulesandthegroupalgebra
1.4reducibility
1.5completereducibilityandmaschke'stheorem
1.6g-homomorphismsandschur'slemma
1.7commutantandendomorphismalgebras
1.8groupcharacters
1.9innerproductsofcharacters
1.10decompositionofthegroupalgebra
1.11tensorproductsagain
1.12restrictedandinducedrepresentations
1.13exercises

2representationsofthesymmetricgroup
2.1youngsubgroups,tableaux,andtabloids
2.2dominanceandlexicographicordering
2.3spechtmodules
2.4thesubmoduletheorem
2.5standardtableauxandabasisfors
2.6garnirelements
2.7young'snaturalrepresentation
2.8thebranchingrule
2.9thedecompositionofmy
2.10thesemistandardbasisforhom（s,m）
2.11kostkanumbersandyoung'srule
2.12exercises

3combinatorialalgorithms
3.1therobinson-schenstedalgorithm
3.2columninsertion
3.3increasinganddecreasingsubsequences
3.4theknuthrelations
3.5subsequencesagain
3.6viennot'sgeometricconstruction
3.7schutzenberger'sjeudetaquin
3.8dualequivalence
3.9evacuation
3.10thehookformula
3.11thedeterminantalformula
3.12exercises

4symmetricfunctions
4.1introductiontogeneratingfunctions
4.2thehillman-grasslalgorithm
4.3theringofsymmetricfunctions
4.4schurfunctions
4.5thejacobi-trudideterminants
4.6otherdefinitionsoftheschurfunction
4.7thecharacteristicmap
4.8knuth'salgorithm
4.9thelittlewood-richardsonrule
4.10themurnnghan-nakayamarule
4.11exercises

5applicationsandgeneralizations
5.1young'slatticeanddifferentialposets
5.2growthsandlocalrules
5.3groupsactingonposets
5.4unimodality
5.5chromaticsymmetricfunctions
5.6exercises
bibliography
index