Cluster algebras and Grassmannians of type G2

Details Cluster algebras and Grassmannians of type G2 Cluster algebras and Grassmannians of type G2

2008-07-26

arxiv.org/abs/0807.4252v2

Algebra and representation theory, volume 13, number 3 (2010)

Mathematics

Representation Theory

minor typos corrected

Scientific paper

10.1007/s10468-008-9126-1

We prove a conjecture of Geiss, Leclerc and Schr\"{o}er, 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.

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