PIRSA:17030081

Braid group symmetries of Grassmannian cluster algebras

Fraser, C. (2017). Braid group symmetries of Grassmannian cluster algebras. Perimeter Institute. https://pirsa.org/17030081

Fraser, Chris. Braid group symmetries of Grassmannian cluster algebras. Perimeter Institute, Mar. 13, 2017, https://pirsa.org/17030081 

          @misc{ pirsa_PIRSA:17030081,
            doi = {10.48660/17030081},
            url = {https://pirsa.org/17030081},
            author = {Fraser, Chris},
            keywords = {Mathematical physics},
            language = {en},
            title = {Braid group symmetries of Grassmannian cluster algebras},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {mar},
            note = {PIRSA:17030081 see, \url{https://pirsa.org}}
          }

Chris Fraser Indiana University

DOI 10.48660/17030081
Collection
Talk Type Scientific Series
Subject

Abstract

We define an action of the k-strand braid group on the set of cluster variables for the Grassmannian Gr(k,n), provided 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). Our results can be translated to statements about clusters in Fock-Goncharov configuration spaces of affine flags, provided the number of flags is even. Finally, we apply our results to the two "Grassmannians of finite mutation type," proving in these cases versions of conjectures made by Fomin and Pylyavskyy describing cluster variables as SL_k web invariants.