Suggestions to study affine and GIT quotients of the extended Grothendieck--Springer resolution

TL;DR

This paper introduces filtered ADHM data and links filtered quiver representations to Grothendieck--Springer resolutions, offering new perspectives and research directions in the study of affine and GIT quotients.

Contribution

It establishes a novel connection between filtered ADHM data and Grothendieck--Springer resolutions, expanding the understanding of these geometric structures.

Findings

Filtered ADHM data is defined and analyzed.

Connections between filtered quiver representations and Grothendieck--Springer resolutions are established.

Research problems for further study of filtered ADHM equations are proposed.

Abstract

We define filtered ADHM data and connect a notion of filtered quiver representations to Grothendieck--Springer resolutions. We also provide current developments and give a list of research problems to further study filtered ADHM equation.