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Symmetric Ideals, Specht Polynomials and Solutions to Symmetric Systems of Equations

hal.structure.identifierInstitut de Mathématiques de Bordeaux [IMB]
dc.contributor.authorMOUSTROU, Philippe
hal.structure.identifierThe Arctic University of Norway [Tromsø, Norway] [UiT]
dc.contributor.authorRIENER, Cordian
hal.structure.identifierThe Arctic University of Norway [Tromsø, Norway] [UiT]
dc.contributor.authorVERDURE, Hugues
dc.date.accessioned2024-04-04T02:57:42Z
dc.date.available2024-04-04T02:57:42Z
dc.date.issued2019-12-11
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/192584
dc.descriptionThis work has been supported by European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement 813211 (POEMA)
dc.description.abstractEnAn ideal of polynomials is symmetric if it is closed under permutations of variables. We relate general symmetric ideals to the so called Specht ideals generated by all Specht polynomials of a given shape. We show a connection between the leading monomials of polynomials in the ideal and the Specht polynomials contained in the ideal. This provides applications in several contexts. Most notably, this connection gives information about the solutions of the corresponding set of equations. From another perspective, it restricts the isotypic decomposition of the ideal viewed as a representation of the symmetric group.
dc.language.isoen
dc.title.enSymmetric Ideals, Specht Polynomials and Solutions to Symmetric Systems of Equations
dc.typeAutre document
dc.subject.halMathématiques [math]
dc.subject.halMathématiques [math]/Géométrie différentielle [math.DG]
dc.subject.halMathématiques [math]/Géométrie algébrique [math.AG]
dc.identifier.arxiv1912.05266
dc.description.sponsorshipEuropePolynomial Optimization, Efficiency through Moments and Algebra
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
hal.identifierhal-02436751
hal.version1
hal.popularnon
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-02436751v1
bordeaux.COinSctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.date=2019-12-11&rft.au=MOUSTROU,%20Philippe&RIENER,%20Cordian&VERDURE,%20Hugues&rft.genre=unknown


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