Equations for GL Invariant Families of Polynomials

Breiding, Paul; Hodges, Reuven; Ikenmeyer, Christian; Michalek, Mateusz

Equations for GL Invariant Families of Polynomials

Dateien

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Datum

2022

Autor:innen

Breiding, Paul

Hodges, Reuven

Ikenmeyer, Christian

Michalek, Mateusz

Open Access-Veröffentlichung

Open Access Hybrid

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Vietnam Journal of Mathematics. Springer. 2022, 50(2), pp. 545-556. ISSN 2305-221X. eISSN 2305-2228. Available under: doi: 10.1007/s10013-022-00549-4

Zusammenfassung

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 Question 7 in Ranestad and Sturmfels (Le Math. 75, 411–424, 2020) and Problem 13 in Sturmfels (2014), 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.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

Defining equations, Highest weight vector, Young tableau, Image of a map, GL-action

Zitieren

ISO 690

BREIDING, Paul, Reuven HODGES, Christian IKENMEYER, Mateusz MICHALEK, 2022. Equations for GL Invariant Families of Polynomials. In: Vietnam Journal of Mathematics. Springer. 2022, 50(2), pp. 545-556. ISSN 2305-221X. eISSN 2305-2228. Available under: doi: 10.1007/s10013-022-00549-4

BibTex

@article{Breiding2022-04Equat-57046,
  year={2022},
  doi={10.1007/s10013-022-00549-4},
  title={Equations for GL Invariant Families of Polynomials},
  number={2},
  volume={50},
  issn={2305-221X},
  journal={Vietnam Journal of Mathematics},
  pages={545--556},
  author={Breiding, Paul and Hodges, Reuven and Ikenmeyer, Christian and Michalek, Mateusz}
}

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