[J._F._Adams]_Lectures_on_Lie_Groups(BookZZ.org)

《[J._F._Adams]_Lectures_on_Lie_Groups(BookZZ.org)》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、LECTURESONLIEGROUPSJFRANKADAMSUniversityofManchesterWABENJAMIN,INCNewYork1969AmsterdamLECTURESONLIEGROUPSCopyright~1969byN.A.Benjamin,Inc.AllrightsreservedStandardBookNumbers.8053-0116-X(Cloth)8053-0117-8(Parer)LibraryofCongressCatalogCardnumber78-84578ManufacturedintheUnitedStatesof

2、America1234R32109ThemanuscriptwasputintoproductiononMarch19,1969thisvolumewaspublishedonJune15,1969.w.A.BENJAMIN,INC.NewYork,NewYork10016CONTENTSPageFOREWORDjxChapter1.BASICDEFINITIONS12.ONE-PARAMETERSUBGROUPSITHEEXPONENTIALMAPIETC.73.ELEMENTARYREPRESENTATIONTHEORY224.MAXIMALTORIINLIE

3、GROUPS795.Gr:OMETRYOFTHESTIEFELDIAGRAM1016.REPRESENTATIONTHEORY1427.REPRESENTATIONSOFTHECIASSICALGROUPS165REFERENCES180viiFOREWORDThesenotesderivefromacourseontherepresentation•theoryofcompactLiegroupswhichIgaveintheUniversityofManchesterin1965,andinparticularfromduplicatednotesonthat

4、coursewhichwerepreparedbyDr.MichaelMather.ItrnaybeaskedwhyonewhoisnotanexpertonLiegroupsshouldreleasesuchacourseforpublication.Theanswerliespartlyintheverylimitedandmodestaimsofthecourse;andpartly,too,inthecontinueddemandfortheduplicatednotes,whichseemstoshowthatanumberofreaderssympat

5、hisewiththeseaims.Ifeelthattherepresen•tation-theoryofcompactLiegroupsisabeautiful,satisfyingandessentiallysimplechapterofmathematics,andthatthereisabasicminimumofitwhichdeservestobeknowntomathematiciansofmanykinds.InmyoriginallecturesIaddressedmyselfmainlytoalgebraictopologists.Ifana

6、lgeb•raictopologisttriestoreadIforexample,BorelandHirzebruch'spaper"CharacteristicClassesandHomogeneousSpaces"[3Jxhefindsthatheneedstoknowthebasicfactsaboutmaximaltori,weightsandrootsofLiegroups.Ifhetriestoread,forexample,BottisIILecturesonK(X)"[4Jhefindsthatheneedstoknowtwomaintheore

7、msontherepresentation-theoryofcompactLiegroups[4,p.50,Theorem1;p.51,Theorem2].Thesetheoremsappear"inmoderndress",buttheygobacktoH.Weyl[22].Ihavegiventheseexamplesforillustration,buttheyarefairlytypical;andtheyhelptoindicateabasicsyllabusonLiegroupswhichmaybeusefultostudentsofmanydiffe

8、rents