Department of Mathematics

Seminar in Cluster algebras

  •  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).

 

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Department of Mathematics
Michigan State University
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East Lansing, MI 48824

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