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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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 |
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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: | |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3144277 |