Grassmannians and Cluster Algebras

Abstract

This paper demonstrates that the homogeneous coordinate ring of the Grassmannian $\mathbb{G}(k,n)$ is a {\it cluster algebra of geometric type} - as defined by S. Fomin and A. Zelevinsky. Grassmannians having {\it finite cluster type} are classified and the associated cluster variables are studied in connection with the geometry of configurations of points in $\mathbb{R}{\mathbb{P}}^2$.

58 pages