Event
Chris Fraser, Indiana University - Purdue University Indianapolis
Braid group symmetries of Grassmannian cluster algebras.
We define an action of the $k$-strand braid group on the set of cluster variables for the Grassmannian Gr$(k,n)$, whenever $k$ divides $n$. The action sends clusters to clusters, preserving the underlying quivers, defining a homomorphism from the braid group to the cluster modular group for Gr$(k,n)$. Then we apply our results to the Grassmannian Gr$(3,9)$. We prove the $n=9$ case of a conjecture of Fomin-Pylyavskyy describing the cluster combinatorics for Gr$(3,n)$, in terms of Kuperberg's basis of non-elliptic webs.