Equations for GL invariant families of polynomials
Abstract
We provide an algorithm that takes as an input a given parametric family of homogeneous polynomials, which is invariant under the action of the general linear group, and an integer . It outputs the ideal of that family intersected with the space of homogeneous polynomials of degree . Our motivation comes from open problems, which ask to find equations for varieties of cubic and quartic symmetroids. The algorithm relies on a database of specific Young tableaux and highest weight polynomials. We provide the database and the implementation of the database construction algorithm. Moreover, we provide a julia implementation to run the algorithm using the database, so that more varieties of homogeneous polynomials can easily be treated in the future.
Keywords
Cite
@article{arxiv.2110.06608,
title = {Equations for GL invariant families of polynomials},
author = {Paul Breiding and Christian Ikenmeyer and Mateusz Michałek and Reuven Hodges},
journal= {arXiv preprint arXiv:2110.06608},
year = {2021}
}