Cluster algebras and Grassmannians of type G2

Abstract

We prove a conjecture of Geiss, Leclerc and Schröer, producing cluster algebra structures on multi-homogeneous coordinate ring of partial flag varieties, for the case $G_2$. As a consequence we sharpen the known fact that coordinate ring of the double Bruhat cell $G^{e,w_0}$ is an upper cluster algebra, by proving that it is a cluster algebra.

minor typos corrected

References in corpus (1)

• Cluster algebras and preprojective algebras : the non simply-laced case

Cited by in corpus (1)

• Examples of quantum cluster algebras associated to partial flag varieties