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Cominuscule flag varieties and their quantum K-theory
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Chung, Sjuvon. Cominuscule flag varieties and their quantum K-theory. Retrieved from https://doi.org/doi:10.7282/T3K35XH6

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TitleCominuscule flag varieties and their quantum K-theory
NameChung, Sjuvon (author); Buch, Anders Skovsted (chair); Weibel, Charles (internal member); Woodward, Christopher (internal member); Lenart, Cristian (outside member); Rutgers University; Graduate School - New Brunswick
Date Created2017
Other Date2017-05 (degree)
SubjectMathematics
Extent1 online resource (v, 39 p. : ill.)
DescriptionThis thesis investigates the ring structure of the torus-equivariant quantum K-theory ring QKT(X) for a cominuscule flag variety X. As a main result, we present an identity that relates the product of opposite Schubert classes in QKT(X) to the minimal degree of a rational curve joining the corresponding Schubert varieties. Using this we infer further properties of the ring QKT(X), one of which is that the Schubert structure constants always sum to one. We also introduce a formula for the quantum product of Schubert classes in projective space Pn. As a corollary we establish Griffeth-Ram positivity of the Schubert structure constants for QKT(Pn). After a closer analysis, we conclude that the rings QKT(Pn) are isomorphic for all n.
NotePh.D.
NoteIncludes bibliographical references
Noteby Sjuvon Chung
Genretheses, ETD doctoral
Persistent URLhttps://doi.org/doi:10.7282/T3K35XH6
Languageeng
CollectionGraduate School - New Brunswick Electronic Theses and Dissertations
Organization NameRutgers, The State University of New Jersey
RightsThe author owns the copyright to this work.
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