Wall-crossing formula for framed quiver moduli

TL;DR

This paper studies how moduli spaces of framed quiver representations change across walls, focusing on type A flag manifolds, Laumon spaces, Nakajima quiver varieties, and sheaves, revealing formulas for their Euler class integrals.

Contribution

It derives explicit wall-crossing formulas for integrals of Euler classes over various framed quiver moduli spaces, connecting geometric changes to representation theory.

Findings

Derived wall-crossing formulas for Euler class integrals

Connected geometric wall-crossing to representation theory

Applied formulas to specific moduli spaces like Laumon spaces

Abstract

We investigate the wall-crossing phenomena for moduli of framed quiver representations. These spaces are expected to be highly useful in capturing the representation theoretic essence of special functions in integrable systems. Within this class of moduli spaces, we focus on the type $A$ flag manifold, type $A$ affine Laumon spaces, Nakajima quiver variety, and framed moduli of sheaves on the projective plane and the blow-up as main motivating examples. Specifically, we examine the wall-crossing formulas for integrals of Euler classes over these moduli spaces.