正規(guī)Siegel域的迷向子群.pdf

1、河南大學(xué)碩士學(xué)位論文正規(guī)Siegel域的迷向子群姓名：馬松雅申請學(xué)位級別：碩士專業(yè)：應(yīng)用數(shù)學(xué)指導(dǎo)教師：許以超王天澤20050501ABSTRACTIn1961，PiatetskiShapiro[1】definedSiegeldomainsandprovedthatanySiegeldomainisholomorphicallyisomorphictoaboundeddomainSuccessivelyin1963，Vinberg，Gin

2、dikinandPiatetskiShapiro[2]provedthatanyhomogeneousboundeddomainisholomorphicallyisomorphictoahomogeneousSiegeldomainIn1976and1977，YichaoXu[31constructedaclassofspecialhomogeneousSiegeldomain，ienormalSiegeldomainD(VN，F(xiàn))，

3、andprovedthatanyhomogeneousSiegeldomainisaffineequivalenttoanormaiSiegeldomainin【4】Alsoin1976，XudeterminedtheLiealgebraaut(D(，Ⅳ，F(xiàn)))oftheholonlorl)hicautomorphismgroupAut(D(V，Ⅳ，F(xiàn)))andthegeneratingelementsoftheaffmeautomor

4、phismgroupAfr(D(I，Ⅳ，F(xiàn)))Atthesametime，Dorfmeistergaveanalge。braicrealizationofahomogeneousboundeddomainandtheholomorphicautomorphismgroup，buttheexistenceconditionofsomeholomorphicautomorphismsinhisworkisnotclearh0211Catmh

5、ySze95kernels(。，i)，Hua[61constructedtheforrealPoissonkernelP(z，i，f，∈)=IS(z，)12／S(z，手)onaclassicaldomain，andprovedthattheformalPoissonkernelisthePoissonkernelfunetionIn1965KoranyiprovedthattheformalPoissonkerilelisthePois

6、sonkernelontimsymmetricSiegeldomainsusingtheLiegrouptheoryWhenDisanindecomposablenormalSiegeldomainXnprovedthataformalPoissonkernelisPoissonkernelifandonlyifDisasymmetricsiegeldomainNotethattheSilovboundaryS(D)ofasymmetr

7、icdomainisatransitiveboundaryactedbytheisotropicsubgroup，butinthecaseofnonsymmetricdomain，theSilovboundaryS(D)isnotatransitiveboundaryactedbytheisotropiesubgroupSowecanposethefollowingproblem：whenDisalion—symmetrichomoge

8、neousSiegeldomainwhatistheintegralrepresenta，tionfromthecontimlousfunctionclassOllSilovboundaryS(D1totheLaplace—BeltramiharmonicfunctionclasswithrespecttotheBergmanmetriconDInordertoconsiderthePoissonintegralweneedtogive

9、theexplicitexpressionsofthefollowine；twosets：oueisthegeneratingelementsofthemaximalconnectedholomorphicautomorphismgroupAut(D(％，F(xiàn)))actingonthenormalSiegeldomains，theotheristhegeneratingelementsoftheisotropicsubgroupIso(D

10、(1哺，F(xiàn)))ofthefixedpoint(~／一1如，O)ParticularlywegivetheexplicitexpressionofailorbitsintheSilovboundaryundertheactionbytheisotropicsubgroupIso(D(h，F(xiàn)))Inthisthesis，wewillgivethegeneratingelementsetoftheisotropicsubgroupIso(D(

11、1k，F(xiàn)))ofthefixedpoint(~／一l”0，o)ThethesisconsistsofthreechaptersChapteronegivesabriefjntroductiontotherelevantbackgroundandposestheproblemwhichwewillsolveinthisthesisChaptertwointroducessomenecessarydefinitionsandtheorems

12、neededforfurtherargumentsInchapterthree，basedonprofessorYichaoXu’swork，weobtainthemainresultsofthisthesis：givesomeoneparametersubgroupsbysolvingsomeordinarydifferentialequationsandgetthegeneratingelementsetofisotropicsub