Subspaces fixed by a nilpotent matrix

Orbita Mathematicae, vol. 1, pp. 1–15

Abstract

The linear spaces that are fixed by a given nilpotent n×n matrix form a subvariety of the Grassmannian.We classify these varieties for small n.Muthiah, Weekes and Yacobi conjectured that their radical ideals are generated by certain linear forms known as shuffle equations.We prove this conjecture for n ≤ 7, and we disprove it for n = 8.The question remains open for nilpotent matrices arising from the affine Grassmannian.

Authors 4

1. Marvin Anas Hahn

   Trinity College Dublin

   Affiliation as printed

   School of Mathematics, Trinity College Dublin, Ireland

2. Gabriele Nebe Aachen Lehrstuhl fuer Algebra und Zahlentheorie

   RWTH Aachen University

   Affiliation as printed

   Lehrstuhl fuer Algebra und Zahlentheorie, RWTH Aachen University, Germany

3. Mima Stanojkovski

   University of Trento

   Affiliation as printed

   Dipartimento di Matematica, Università di Trento, Italy

4. Bernd Sturmfels

   Max Planck Institute for Mathematics in the Sciences · University of California, Berkeley

   Affiliation as printed

   Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, University of California at Berkeley, California, United States