Department of Mathematics

Seminar in Cluster algebras

  •  Categorification of cluster structure on partial flag varieties
  •  10/25/2016
  •  1:00 PM - 1:50 PM
  •  C304 Wells Hall
  •  Maitreyee Kulkarni, Louisiana State University

Let G be a Lie group of type ADE and P be a parabolic subgroup. It is known that there exists a cluster structure on the coordinate ring of the partial flag variety G/P (see the work of Geiss, Leclerc, and Schroer). Since then there has been a great deal of activity towards categorifying these cluster algebras. Jensen, King, and Su gave a direct categorification of the cluster structure on the homogeneous coordinate ring for Grassmannians (that is, when G is of type A and P is a maximal parabolic subgroup). In this setting, Baur, King, and Marsh gave an interpretation of this categorification in terms of dimer models. In this talk, I will give an analog of dimer models for groups in other types by introducing a technique called “constructing sheets over Dynkin diagrams”, which can (conjecturally) be used to generalize the result of Baur, King, and Marsh.

 

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Department of Mathematics
Michigan State University
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C212 Wells Hall
East Lansing, MI 48824

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