Equivariant resolutions of singularities for orbits in generalized quiver varieties arising in the local Langlands program for p-adic groups

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dc.contributor.authorBenesh, Joel L. E.
dc.contributor.authorUniversity of Lethbridge. Faculty of Arts and Science
dc.contributor.supervisorFiori, Andrew
dc.date.accessioned2023-03-06T17:00:29Z
dc.date.available2023-03-06T17:00:29Z
dc.date.issued2022
dc.degree.levelMastersen_US
dc.description.abstractIn this thesis, we investigate geometric aspects of the Langlands parameters arising in the local Langlands Program for p-adic groups. This work was inspired by David Vogan’s “The Local Langlands Conjecture”, and we built off of the work of Clifton Cunningham, Andrew Fiori, Ahmed Moussaoui, James Mracek, and Bin Xu in their book “Arthur Packets for p-Adic Groups by Way of Microlocal Vanishing Cycles of Perverse Sheaves, with Examples”. This thesis follows the construction detailed in Part II of their book, and we give more concrete examples to demonstrate their construction. Additionally, we provide an exposition on the local Langlands program for p-adic groups and give an algorithm for computing the resolutions of singularities arising from the study of the orbits of certain generalized quiver varieties for their respective Langlands parameters in the groups GLn, SOn, and Sp2n.en_US
dc.identifier.urihttps://hdl.handle.net/10133/6448
dc.language.isoen_USen_US
dc.proquest.subject0405en_US
dc.proquestyesYesen_US
dc.publisherLethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Science
dc.publisher.departmentDepartment of Mathematics & Computer Scienceen_US
dc.publisher.facultyArts and Scienceen_US
dc.relation.ispartofseriesThesis (University of Lethbridge. Faculty of Arts and Science)
dc.subjectp-adic groups
dc.subjectLanglands parameters
dc.subjectlocal Langlands program
dc.subjectresolutions of singularities
dc.subjectgeneralized quiver varieties
dc.subjectorbit algebra
dc.subjectreductive algebraic groups
dc.subjectp-adic groups
dc.subjectSingularities (Mathematics)
dc.subjectOrbit method
dc.subjectGeometry
dc.subjectAlgebraic
dc.subjectArithmetical algebraic geometry
dc.subjectRepresentations of groups
dc.subjectDirected graphs
dc.subjectDissertations
dc.subjectAcademic
dc.titleEquivariant resolutions of singularities for orbits in generalized quiver varieties arising in the local Langlands program for p-adic groupsen_US
dc.typeThesisen_US
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