- Braid Group Symmetries of Grassmannian Cluster Algebras
- 04/25/2017
- 2:00 PM - 2:50 PM
- C304 Wells Hall
- Chris Fraser, IUPUI
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 Grassmannians of 'finite mutation type'. 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, and prove a similar result for the Grassmannian Gr(4,8).