Combinatorial approach to ABV-packets for GLn

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dc.contributor.authorRiddlesden, Connor David
dc.contributor.authorUniversity of Lethbridge. Faculty of Arts and Science
dc.contributor.supervisorFiori, Andrew
dc.date.accessioned2022-11-03T22:08:09Z
dc.date.available2022-11-03T22:08:09Z
dc.date.issued2022
dc.degree.levelMastersen_US
dc.description.abstractThere exists a significant conjecture in the local Langlands correspondence that A-packets are ABV-packets. For the case G=GLn, the conjecture reduces to ABV-packets for orbits of Arthur type being singletons, which is a specialisation of the wider conjecture known as the Open-Orbit conjecture. We can reduce the complexity of this problem by considering the combinatorial geometry of these objects using multisegments, since there exists a natural relationship between this description and the structure of ABV-packets. The first part of this thesis investigates interpretations of the Zelevinskii Involution. We then use combinatorial approaches involving endoscopic decompositions and numerical invariants to study the partial ordering in the Open-Orbit conjecture, which will lead to the proof that ABV- packets for orbits of Arthur type in GLn are singletons. Finally, we use a numerical-based argument to conjecture families of ABV-packets for which the partial ordering relation is not satisfied for.en_US
dc.identifier.urihttps://hdl.handle.net/10133/6377
dc.language.isoen_USen_US
dc.proquest.subject0405en_US
dc.proquestyesYesen_US
dc.publisherLethbridge, Alta. : University of Lethbridge, Dept. of Mathematics and Computer Scienceen_US
dc.publisher.departmentDepartment of Mathematics and Computer Scienceen_US
dc.publisher.facultyArts and Scienceen_US
dc.relation.ispartofseriesThesis (University of Lethbridge. Faculty of Arts and Science)en_US
dc.subjectmathematicsen_US
dc.subjectABV-packetsen_US
dc.subjectcombinatorial geometryen_US
dc.subjectOpen-Orbit conjectureen_US
dc.subjectZelevinskii involutionen_US
dc.subjectmultisegmentsen_US
dc.subjectendoscopic decompositionen_US
dc.subjectnumerical invariantsen_US
dc.subjectAlgebraen_US
dc.subjectCombinatorial geometryen_US
dc.subjectNumber theoryen_US
dc.subjectRepresentations of groupsen_US
dc.subjectDissertations, Academicen_US
dc.titleCombinatorial approach to ABV-packets for GLnen_US
dc.typeThesisen_US
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