×

Purity of critical cohomology and Kac’s conjecture. (English) Zbl 1419.16010

Summary: We provide a new proof of the Kac positivity conjecture for an arbitrary quiver \(Q\). The ingredients are the cohomological integrality theorem in Donaldson-Thomas theory, dimensional reduction, and an easy purity result. These facts imply the purity of the cohomological Donaldson-Thomas invariants for partially nilpotent representations of a quiver with potential \((\widetilde{Q},W)\) associated to \(Q\), which in turn implies positivity of the Kac polynomials for \(Q\).

MSC:

16G20 Representations of quivers and partially ordered sets
05E10 Combinatorial aspects of representation theory
PDFBibTeX XMLCite
Full Text: DOI arXiv