Abstracts for the Seminar
 Discrete Geometry and Combinatorics
 Fall 2017

Speaker:  Tair Akhmejanov, Cornell University
Title: Affine growth diagrams
Time: 2:30 PM, Monday, September 17, 2017
Place:  Malott 206

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 $c_{\vec\lambda}$ many components of the polygon space Poly($\vec\lambda$) for $\vec\lambda$ a sequence of minuscule weights and $c_{\vec\lambda}$ the Littlewood--Richardson coefficient. 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 $n$-hive of Knutson-Tao-Woodward.

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