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dc.contributor.authorAkhmejanov, Tair
dc.identifier.otherbibid: 10489669
dc.description.abstractWe introduce growth diagrams 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. 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. Similar diagrams appeared in the work of Speyer on osculating flags.
dc.titleGrowth Diagrams from Polygons in the Affine Grassmannian
dc.typedissertation or thesis University of Philosophy D., Mathematics
dc.contributor.chairKnutson, Allen
dc.contributor.committeeMemberKozen, Dexter Campbell
dc.contributor.committeeMemberStillman, Michael Eugene

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