Framed moduli spaces and tuples of operators

TL;DR

This paper develops a classification scheme for tuples of linear operators and functions on finite-dimensional vector spaces using framed moduli spaces of quivers, providing explicit normal forms and an equivalence procedure.

Contribution

It introduces a novel approach using framed moduli spaces to classify operator tuples, offering explicit normal forms and an algorithm for equivalence determination.

Findings

Explicit classification of tuples in a Zariski open subset

Finite normal forms for classified tuples

Procedure to determine tuple equivalence

Abstract

In this work we address the classical problem of classifying tuples of linear operators and linear functions on a finite dimensional vector space up to base change. Having adopted for the situation considered a construction of framed moduli spaces of quivers, we develop an explicit classification of tuples belonging to a Zariski open subset. For such tuples we provide a finite family of normal forms and a procedure allowing to determine whether two tuples are equivalent.