资源描述：
《Garsia and Stanton---Group actions on Stanley-Reisner rings and invariants of permutation groups.pdf》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、ADVANCESINMATHEMATICS51,107-201(1984)GroupActionsonStanley-ReisnerRingsandInvariantsofPermutationGroups*A.M.GARSIAANDD.STANTONDepartmentofMathematics,UniversityofCaliforniaatSanDiego,SanDiego.Calfornia92093LetHbeagroupofpermutationsofx,,...,x,andletQ”
2、]x,,x1,....x,]denotetheringofH-invariantPolynomialsinx,,x2....,X,withrationalcoefftcients.CombinatorialmethodsfortheexplicitconstructionoffreebasesforQ”[.q,x2....,x”]asamoduleoverthesymmetricpolynomialsaredeveloped.Themethodsaredevelopedbystudyingthea
3、ctionofthesymmetricgroupontheStanley-Reisnerringofthesubsetlattice.SomegeneralresultsarealsoobtainedbystudyingtheactionofaCoxetergroupontheStanley-ReisnerringofthecorrespondingCoxetercomplex.InthecaseofaWeylgroup.apurelycombinatorialconstructionofcert
4、aininvariantsfirstconsideredbyR.Steinberg(Topology14(1975).173-177)isobtained.Someapplicationstorepresentationtheoryarealsoincluded.Contents.Introduction.0.Preliminaries.1.TheactionofGinH,(R,).2.TheactionofGinR,/(O,,...,0,).3.TheHilbertseriesofRF.4.Co
5、hen-MacaulaynessofthemodulesReR,.5.Criteriaforthedirectconstructionofbasicsets.6.ThequotientBooleanComplex.7.Theactionofthesymmetricgroup.8.TheactionofaWeylgroup.9.Invariantsinthestandardpolynomialring.10.Applicationstorepresentationtheory.LetQ[x,,...
6、,xn]denotetheringofpolynomialsinx,,...,x,withrationalcoeffkients.Forapermutation12*.*nCT=a,(T2...unandapolynomialPEQ[x,,...,x,,]wesetUP(X)=P(x,,,x,,,....X,“).*ThisworkwascarriedoutunderthesupportofNSFgrants.107OOOl-8708/84$7.50CopyrightQ1984byAcademic
7、Press.Inc.Allrightsofreproductioninanyformreserved.108GARSIAANDSTANTONGivenasubgroupHofthesymmetricgroupS,wesaythatPEQIx,,...,x,,]isH-invariantifandonlyifaP=P(forallcsEH).TheS,-invariantpolynomialsareofcourseusuallyreferredtoassymmetric.Itisawell-know
8、nclassicalresultthateverysymmetricpolynomialPcanbeexpressedintheformwhereUk=UJX)=cxi,xi,.*.Xik’I
