Symmetric Ideals, Specht Polynomials and Solutions to Symmetric Systems of Equations
Langue
en
Autre document
Ce document a été publié dans
2019-12-11
Résumé en anglais
An 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 ...Lire la suite >
An 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.< Réduire
Projet Européen
Polynomial Optimization, Efficiency through Moments and Algebra
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