dc.contributor.author Akhmejanov, Tair dc.date.accessioned 2018-10-23T13:33:38Z dc.date.available 2018-10-23T13:33:38Z dc.date.issued 2018-08-30 dc.identifier.other Akhmejanov_cornellgrad_0058F_10894 dc.identifier.other http://dissertations.umi.com/cornellgrad:10894 dc.identifier.other bibid: 10489669 dc.identifier.uri https://hdl.handle.net/1813/59573 dc.description.abstract We 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.language.iso en_US dc.subject Mathematics dc.title Growth Diagrams from Polygons in the Affine Grassmannian dc.type dissertation or thesis thesis.degree.discipline Mathematics thesis.degree.grantor Cornell University thesis.degree.level Doctor of Philosophy thesis.degree.name Ph. D., Mathematics dc.contributor.chair Knutson, Allen dc.contributor.committeeMember Kozen, Dexter Campbell dc.contributor.committeeMember Stillman, Michael Eugene dcterms.license https://hdl.handle.net/1813/59810 dc.identifier.doi https://doi.org/10.7298/X4MK6B3G
﻿