Date: Friday, December 08, 2017
Location: 4088 East Hall (4:10 PM to 5:00 PM)
Title: Affine Growth Diagrams
Abstract: We introduce a new type of growth diagram, arising from the geometry of the affine Grassmannian for GL_m. These affine growth diagrams are in bijection with the components of the polygon space for a sequence of minuscule weights. Unlike Fomin growth diagrams, they are infinite periodic on a staircase shape, and each vertex is labeled by a dominant weight of GL_m. Letting m go to infinity, a dominant weight can be viewed as a pair of partitions, and we recover the RSK correspondence and Fomin growth diagrams within affine growth diagrams. The main combinatorial tool used in the proofs is the nhive of KnutsonTaoWoodward. The local growth rule satisfied by the diagrams previously appeared in van Leeuwen's work on Littelmann paths, so our results can be viewed as a geometric interpretation of this combinatorial rule.
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Speaker: Tair Akhmejanov
Institution: Cornell
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