Grassmannians and Cluster Algebras

Details Grassmannians and Cluster Algebras Grassmannians and Cluster Algebras

2003-11-10

arxiv.org/abs/math/0311148v1

Mathematics

Combinatorics

58 pages

Scientific paper

This paper demonstrates that the homogeneous coordinate ring of the
Grassmannian $\Bbb{G}(k,n)$ 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 $\Bbb{R}\Bbb{P}^2$.

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