階化Cartan型李代數(shù)W（m;n）的I（X）-誘導(dǎo)表示.pdf

1、華東師范大學(xué)碩士學(xué)位論文階化Cartan型李代數(shù)W（mn）的I（X）誘導(dǎo)表示姓名：李莎莎申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：基礎(chǔ)數(shù)學(xué)指導(dǎo)教師：舒斌20050401ABSTRAeTInthispaper，wediscusstherepresentationofCaftantypeLiealgebraW(ra；n)incharacteristicP2，fromtheviewpointofreducingrankWhenthecharacterXisre

2、gularsemisimple，wecallreducehigerrankrepresentationstolower—rankrepresentationsBecausethegradedCartantpyeLiealgebra￡=彤橛；n)isnotarestrictedLiealgebrawhenn≠l，Kac—Weisfeiler’Smethodofdividingtheirreduciblemoduleswithcharact

3、erfunctionsisnotworkThankstothediscussofgeneralizedrestrictedLiealgebrasbyShuBin，wehaveknownthatthegeneralizedrestrictedxreducedmodulecategorycoincideswiththeTreducedmodulecategoryofitsprimitivepenvelope，where躉isthetrivi

4、alextensionofXintheprimitivepenvelope。SowecandescribetheirreduciblerepresentationofL—W(m；n)bydiscussingtheirreduciblerepresentationofitsprimitivepenvelope￡=L∑罌l∑簍；芯拶妒啦。Forallindexsubset，C1，2，，”矗anditssupplementjc1，2，，m)＼

5、，，wehavethedividedpoweralgebra2【(J『)andthetwogeneralized、：Vitta1gebrasw(1)andW(j)，F(xiàn)oranyLiealgebra垂，wecandefinealoopalgebraassociatedwithadividedalgebra躡：疆圓gWecanreducetherepresentationof￡totherepresentationofitsgradedLi

6、esubalgebra￡酬，f一島ow(j)@磁(髟◇蠡f(j)，where舀=∑蜒j∑裟三甕雄冷。w(hand毋normalizeeachloopsubalgebraof2I(J『)@w(nThismakesitpossibletoconsidersomeinducedrepresentationsrelatedtoW(I)andⅣ(f)FromthisviewpointwecaD_reducetherepiesentationof上