Equations for GL Invariant Families of Polynomials

Breiding, Paul, Hodges, Reuven, Ikenmeyer, Christian and Michalek, Mateusz (2022) Equations for GL Invariant Families of Polynomials. VIETNAM JOURNAL OF MATHEMATICS, 50 (2). pp. 545-556.

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Official URL: http://dx.doi.org/10.1007/s10013-022-00549-4

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 $d$. It outputs the ideal of that family intersected with the space of homogeneous polynomials of degree $d$. 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.

Item Type:	Article
Uncontrolled Keywords:	Defining equations, Highest weight vector, Young tableau, Image of a map, GL-action
Divisions:	Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User:	Symplectic Admin
Date Deposited:	01 Dec 2021 09:22
Last Modified:	18 Jan 2023 21:23
DOI:	10.1007/s10013-022-00549-4
Open Access URL:	https://link.springer.com/article/10.1007/s10013-0...
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3144277