Affine Pavings of Hessenberg Ideal Fibers

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dc.contributor.advisorBrosnan, Patricken_US
dc.contributor.authorXue, Keen_US
dc.contributor.departmentMathematicsen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.date.accessioned2020-09-25T05:35:42Z
dc.date.available2020-09-25T05:35:42Z
dc.date.issued2020en_US
dc.description.abstractWe define certain closed subvarieties of the flag variety, Hessenberg ideal fibers, and prove that they are paved by affines. Hessenberg ideal fibers are a natural generalization of Springer fibers. In type $G_2$, we give explicit descriptions of all Hessenberg ideal fibers, study some of their geometric properties and use them to completely classify Tymoczko's dot actions of the Weyl group on the cohomology of regular semisimple Hessenberg varieties.en_US
dc.identifierhttps://doi.org/10.13016/evqm-0y32
dc.identifier.urihttp://hdl.handle.net/1903/26442
dc.language.isoenen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pquncontrolledaffine pavingen_US
dc.subject.pquncontrolleddot actionen_US
dc.subject.pquncontrolledflag varietyen_US
dc.subject.pquncontrolledHessenberg varietyen_US
dc.subject.pquncontrolledSpringer fiberen_US
dc.subject.pquncontrolledTymoczkoen_US
dc.titleAffine Pavings of Hessenberg Ideal Fibersen_US
dc.typeDissertationen_US

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