24456.典型李代數(shù)在一般線性群上的表示理論

1、分類號一UDC密級鍪開一Z毋聲夕乎碩士研究生學(xué)位論文典型李代數(shù)在一般線性群上的表示理論申請人：寧玉琪學(xué)號：2111068培養(yǎng)單位：數(shù)學(xué)科學(xué)學(xué)院學(xué)科專業(yè)：基礎(chǔ)數(shù)學(xué)研究方向：李代數(shù)指導(dǎo)教師：唐孝敏教授完成日期：2014年3月12日AbstractAs1swell—known，8tudytherepre8entationofanalgebraiccanstudyfromw1。hln‘healgebra(thatis，researchonthe

2、algebr缸crepresentationspace)，canstudy打om。heoutsideofthealgebra(thatis，StudytheaIgebraasarepre8entationspace)’IhispaperwiUstudyr印resentatjonofthegenerallinearliealgebragZ(3，C)tromou‘slde。Ihispaperwillgetgenerallineaurliea

3、lgebra∥(3，c)ing鉍erallineargroupsG己(2，c)allkindsofsaidstructureThisnotonlystudyingthetheori鋁ofthegeneral1jnearliealgebras∥(3，c)：willalso百vesomerealizeof9dimensionalrepresentationofthegenerallineargroupGL(2，c)P1rstlyusepr叩

4、ertiesofconjugaterepresentationtoke印trackandmultiDlicatlonofpartitionedmatrixmethodsi8百ven出lirreduciblesubmodulesof鰣(3：C)Bythe8pace0fknoWledgecanbeprovedthaLttheconjugater印reseIltationiscomsec。nmy，because。fthesymmetricma

5、trixandantis)rIIlmetricmatri)【inthetransp。8edrepresentati。ncanc。nstituteasubm。dule。鉚(3；c)Acc。rdingt。thischarac‘eristiccanberes。lVeGL(2；c)一m。dule9f(3；c)int。thedirectlyofirreducibler印resentatjonThispapern。t。nlypr。motedthed