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图书标准信息

• 作者 [德]韦尔 著
• 出版社 世界图书出版公司
• 出版时间 2011-01
• 版次 1
• ISBN 9787510029592
• 定价 39.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 320页
• 正文语种 英语
• 原版书名 The Classical Groups: Their Invariants and Representations

【内容简介】

Eversincetheyear1925，whenIsucceededindeterminingthecharactersofthesemi-simplecontinuousgroupsbyacombinationofE.Cartansinfini-tesimalmethodsandI.Schursintegralprocedure，Ihavelookedtowardthegoalofderivingthedecisiveresultsforthemostimportantofthesegroupsbydirectalgebraicconstruction，inparticularforthefullgroupofallnon-singu-larlineartransformationsandfortheorthogonalgroup.OwingmainlytoR.Brauersinterventionandcollaborationduringthelastfewyears，itnowappearsthatIhaveinmyhandsallthetoolsnecessaryforthispurpose.Thetaskmaybecharacterizedpreciselyasfollows：withrespecttotheassignedgroupoflineartransformationsintheunderlyingvectorspace，todecomposethespaceoftensorsofgivenrankintoitsirreducibleinvariantsubspaces.

【目录】

TABLEOFCONTENTS
PREFACETOTHEFIRSTEDITION
PREFACETOTHESECONDEDITION
CHAPTERI
INTRODUCTION
1.Fields，rings，ideals，polynomials
2.Vectorspace
3.Orthogonaltransformations，Euclideanvectorgeometry
4.Groups，KleinsErlangerprogram..Quantities
5.Invariantsandcovariants
CHAPTERII
VECTORINVARIANTS
1.Remembranceofthingspast
2.Themainpropositionsofthetheoryofinvariants
A.FrostMAINTHEOREM
3.Firstexample：thesymmetricgroup
4.Capellisidentity
5.ReductionofthefirstmainproblembymeansofCapellisidentities
6.Secondexample：theunimodulargroup，.qL（n）
7.Extensiontheorem.Thirdexample：thegroupofsteptransformations
8.Ageneralmethodforincludingeontravariantarguments
9.Fourthexample：theorthogonalgroup
B.ACLOSE-UPOFTHEORTHOGONALGROUP
10.Cayleysrationalparametrizationoftheorthogonalgroup
11，Formalorthogonalinvariants
12.Arbitrarymetricgroundform
13.Theinfinitesimalstandpoint
C.THESECONDMAINTHEOREM
14.Statementofthepropositionfortheunimodulargroup
15.Capellisformalcongruence
16.Proofofthesecondmaintheoremfortheunimodulargroup
17.Thesecondmaintheoremfortheunimodulargroup
CHAPTERIII
MATRICALGEBRASANDGROUPRINGS
A.THEORYOFFULLYREDUCIBLEMATRICALGEBRAS
1.Fundamentalnotionsconcerningmatricalgebras.TheSchurlemma
2.Preliminaries
3.Representationsofasimplealgebra
4.Wedderburnstheorem
5.Thefullyreduciblematricalgebraanditscommutatoralgebra
B.THERINGOFAFINITEGROUPANDITSCOMMUTATORALGEBRA
6.Statingtheproblem
7.Fullreducibilityofthegroupring
TABLEOFCONTENTS
8.Formallemmas.
9.Reciprocitybetweengroupringandcommutatoralgebra
10.Ageneralization
CHAPTERIV
THESYMMETRICGROUPANDTHEFULLLINEARGROUP
1.Representationofafinitegroupinanalgebraicallyclosedfield
2.TheYoungsymmetrizers.Acombinatoriallsmma
3.Theirreduciblerepresentationsofthesymmetricgroup
4.Decompositionoftensorspace
5.Quantities.Expansion
CHAPTERV
THEORTHOGONALGROUP
A.THEENVELOPINGALGEBRAANDTHEORTHOGONALIDEAL
1.Vectorinvariantsoftheunimodulargroupagain
2.Theenvelopingalgebraoftheorthogonalgroup
3.Givingtheresultitsformalsetting
4.Theorthogonalprimeideal
5.Anabstractalgebrarelatedtotheorthogonalgroup
B.THEIRREDUCIBLEREPRESENTATIONS
6.Decompositionbythetraceoperation
7.Theirreduciblerepresentationsofthefullorthogonalgroup
C.THEPROPERORTHOGONALGROUP
8.Cliffordstheorem
9.Representationsoftheproperorthogonalgroup
CHAPTERVI
THESYMPLECTICGROUP
1.Vectorinvariantsofthesymplecticgroup
2.Parametrizationandunitaryrestriction
3.Embeddingalgebraandrepresentationsofthesymplecticgroup
CHAPTERVII
CHARACTERS
1.Preliminariesaboutunitarytransformations
2.Characterforsymmetrizationoralternationalone
3.Averagingoveragroup
4.Thevolumeelementoftheunitarygroup
5.Computationofthecharacters
6.ThecharactersofGL（n）.Enumerationofcovariants
7.Apurelyalgebraicapproach
8.Charactersofthesymplecticgroup
9.Charactersoftheorthogonalgroup
10.DecompositionandX-multiplication
11.ThePoinear~polynomial
……