Computational Methods for Orbit Closures in a Representation with Finitely Many Orbits

Abstract

The action of on has finitely many orbits. Kraśkiewicz and Weyman give a conjectural description of the minimal free resolution of the coordinate ring for certain orbit closures in . We verify their conjecture by constructing their complexes explicitly in Macaulay2 and checking that they are exact. We also construct equations for all the orbit closures and verify that they generate radical ideals.

2000 AMS Subject Classification::

• 13D02
• 13P99
• 14M17
• 20G05

Keywords::

• trilinear alternating forms
• orbit closures
• equivariant maps
• exactness criterion
• geometric technique
• Macaulay2

Notes

¹Macaulay2 is available at http://www.math.uiuc.edu/Macaulay2/.

²Available at http://www-math.univ-poitiers.fr/maavl/LiE/.

³All computations were performed on a 2013 Macbook Air with a Core i7 processor and 8 GB of RAM, running Mac OS X 10.9 and Macaulay2 1.6.