Transfer of Representations and Orbital Integrals of Inner Forms of GL_n
dc.contributor.advisor | Haines, Thomas J. | en_US |
dc.contributor.author | Cohen, Jonathan | en_US |
dc.contributor.department | Mathematics | en_US |
dc.contributor.publisher | Digital Repository at the University of Maryland | en_US |
dc.contributor.publisher | University of Maryland (College Park, Md.) | en_US |
dc.date.accessioned | 2017-06-22T06:16:00Z | |
dc.date.available | 2017-06-22T06:16:00Z | |
dc.date.issued | 2016 | en_US |
dc.description.abstract | Let $F$ be a nonarchimedean local field and $D$ an $F$-central division algebra. We characterize the Local Langlands Correspondence (LLC) for inner forms of $GL_n$ over $F$ via the Jacquet-Langlands Correspondence and compatibility with the Langlands Classification. We show that LLC satisfies a natural compatibility with parabolic induction and characterize the LLC for inner forms as a unique family of bijections $\Pi(GL_r(D)) \rightarrow \Phi(GL_r(D))$ for each $r$, (for a fixed $D$) satisfying certain properties. We construct a surjective map of Bernstein centers $\mathfrak{Z}(GL_n(F))\to \mathfrak{Z}(GL_r(D))$ and show this produces pairs of matching distributions in the sense of \cite{SBC}. Finally, we construct explicit Iwahori-biinvariant matching functions for unit elements in the parahoric Hecke algebras of $GL_r(D)$, and thereby produce many explicit pairs of matching functions. | en_US |
dc.identifier | https://doi.org/10.13016/M2CZ8R | |
dc.identifier.uri | http://hdl.handle.net/1903/19450 | |
dc.language.iso | en | en_US |
dc.subject.pqcontrolled | Mathematics | en_US |
dc.subject.pquncontrolled | GL_n | en_US |
dc.subject.pquncontrolled | Inner Forms | en_US |
dc.subject.pquncontrolled | Local Langlands | en_US |
dc.title | Transfer of Representations and Orbital Integrals of Inner Forms of GL_n | en_US |
dc.type | Dissertation | en_US |
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