2017/06/15 by Ben Johnson, Ben A. Johnson, Eric Sommers +2 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.AG #math.RT
paper · pdf · doi:10.48550/arxiv.1706.04820
25 pages, 1 figure. Some minor corrections and additional references in the appendices
openalex publication_date 2017/06/15 · arxiv created 2018/02/05 · arxiv updated 2018/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let O be a Richardson nilpotent orbit in a simple Lie algebra \mathfrakg over \mathbb C, induced from a Levi subalgebra whose simple roots are orthogonal short roots. The main result of the paper is a description of a minimal set of generators of the ideal defining O in S \mathfrakg^*. In such cases, the ideal is generated by bases of at most two copies of the representation whose highest weight is the dominant short root, along with some fundamental invariants. This extends Broer's result for the subregular nilpotent orbit. Along the way we give another proof of Broer's result that O is normal. We also prove a result connecting a property of invariants related to flat bases to the question of when one copy of the adjoint representation is in the ideal in S \mathfrakg^* generated by another copy of the adjoint representation and the fundamental invariants.