Minimal Set of Generators of Ideals Defining Nilpotent Orbit Closures

TL;DR

This paper constructs a minimal generating set for the ideals defining nilpotent orbit closures in matrices over characteristic zero fields, resolving a conjecture by Weyman.

Contribution

It provides a complete construction of minimal generators for nilpotent orbit closure ideals, advancing understanding of their algebraic structure.

Findings

Complete minimal generating set constructed

Resolved Weyman's conjecture

Clarified algebraic structure of nilpotent orbit closures

Abstract

Over a field of characteristic $0$, we construct a minimal set of generators of the defining ideals of closures of nilpotent conjugacy class in the set of $n \times n$ matrices. This modifies a conjecture of Weyman and provides a complete answer to it.