# 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.date.accessioned 2017-06-22T06:16:00Z dc.date.available 2017-06-22T06:16:00Z dc.date.issued 2016 en_US dc.identifier https://doi.org/10.13016/M2CZ8R dc.identifier.uri http://hdl.handle.net/1903/19450 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.language.iso en en_US dc.title Transfer of Representations and Orbital Integrals of Inner Forms of GL_n en_US dc.type Dissertation 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.contributor.department Mathematics 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
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