Counting Using Hall Algebras I. Quivers
arXiv:1111.6452
Abstract
We survey some results on counting the rational points of moduli spaces of quiver representations. We then make generalizations to Grassmannians and flags of quiver representations. These results have nice applications to the cluster algebra. Along the way, we use the full Hopf structure of the Hall algebra of a quiver.
18 pages, final version to appear in J. Algebra. A minor mistake in "Quantum Cluster Algebra" section was corrected; reference updated