Symmetric Ideals, Specht Polynomials and Solutions to Symmetric Systems of Equations
Language
en
Autre document
This item was published in
2019-12-11
English Abstract
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 ...Read more >
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.Read less <
European Project
Polynomial Optimization, Efficiency through Moments and Algebra
Origin
Hal imported