Separating invariants of three nilpotent 3x3 matrices

TL;DR

This paper identifies a minimal set of invariants that can distinguish between different triples of 3x3 nilpotent matrices under conjugation, advancing understanding of their algebraic structure.

Contribution

It provides a minimal separating set for the algebra of invariants of three 3x3 nilpotent matrices under conjugation, a case previously not fully characterized.

Findings

Established a minimal separating set for the algebra of invariants

Extended the understanding of invariants for nilpotent matrices

Contributed to the theory of matrix invariants in algebraic geometry

Abstract

The algebra of GL_n-invariants of d-tuple of n x n nilpotent matrices with respect to the action by simultaneous conjugation is generated by the traces of products of nilpotent generic matrices in the case of an algebraically closed field of characteristic zero. We described a minimal separating set for this algebra in case n=d=3.