Landau-Ginzburg potentials via projective representations

TL;DR

This paper links Landau-Ginzburg potentials to F-polynomials of projective representations in cluster algebra theory, demonstrating their behavior under mutations and providing new insights into Jacobian algebras.

Contribution

It introduces a novel interpretation of Landau-Ginzburg potentials as F-polynomials of projective representations and studies their mutation behavior in Jacobian algebras.

Findings

Landau-Ginzburg potentials are interpreted as F-polynomials of projective representations.

Projective and injective representations are well-behaved under mutations.

Provides a new perspective on cluster varieties and their compactifications.

Abstract

We interpret the Landau-Ginzburg potentials associated to Gross-Hacking-Keel-Kontsevich's partial compactifications of cluster varieties as F-polynomials of projective representations of Jacobian algebras. Along the way, we show that both the projective and the injective representations of Jacobi-finite quivers with potential are well-behaved under Derksen-Weyman-Zelevinsky's mutations of representations.