Special Unipotent Arthur Packets for Real Reductive Groups

Simple item page
dc.contributor.advisorAdams, Jeffrey Den_US
dc.contributor.authorFernandes, Jonathan Francisen_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.accessioned2019-09-26T05:33:56Z
dc.date.available2019-09-26T05:33:56Z
dc.date.issued2019en_US
dc.description.abstractLet $\GR$ be a real reductive group. In this thesis we study the unitary representations of $\GR$. In particular, we study the special Arthur unipotent parameters and the associated packets of irreducible representations of $\GR$. It is conjectured that these unipotent representations form the building blocks for all unitary representations of $\GR$. \\ To understand unipotent representations, we will need to compute the following invariants of irreducible representations of $\GR$: complex associated variety and the theta associated variety. Even though these invariants are theoretically understood, there are no known (at least to this author) results/algorithms to compute them explicitly. \\ The primary results of this thesis provide algorithms to compute these invariants explicitly in many cases. We then use these invariants to compute information about unipotent Arthur packets, and in favorable cases, their entire contents explicitly. In unfavorable cases, we show how to extract more information from our results by using the stable sum formula. \\ We have implemented these algorithms into the Atlas of Lie Groups software, available at www.liegroups.org. We also provide some tables of data compiled using the output from Atlas.en_US
dc.identifierhttps://doi.org/10.13016/qmf9-ntwp
dc.identifier.urihttp://hdl.handle.net/1903/24947
dc.language.isoenen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pquncontrolledArthur Packetsen_US
dc.subject.pquncontrolledAssociated Varietiesen_US
dc.subject.pquncontrolledLie Groupsen_US
dc.subject.pquncontrolledUnipotent Packetsen_US
dc.subject.pquncontrolledUnitary Dualen_US
dc.subject.pquncontrolledUnitary Representationsen_US
dc.titleSpecial Unipotent Arthur Packets for Real Reductive Groupsen_US
dc.typeDissertationen_US

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
Fernandes_umd_0117E_20207.pdf
Size:
573.67 KB
Format:
Adobe Portable Document Format
Download

Collections

UMD Theses and Dissertations
Mathematics Theses and Dissertations