title: Boundary Distributions for GL3 over a Local Field and  Symmetric Power Coefficients
creator: Gräf, Peter Mathias
subject: ddc-510
subject: 510 Mathematics
description: In this thesis, we construct a residue map and a Poisson kernel between holomorphic discrete series representations on the Drinfeld period domain and harmonic cocycles with certain non-trivial coefficients on the Bruhat-Tits building for GL3 over a local field of any characteristic. In order to construct the Poisson kernel, we find a new locally analytic kernel function that can be integrated against general boundary distributions. Assuming the existence of certain boundary distributions attached to bounded harmonic  cocycles, we prove that the Poisson kernel is a right inverse of the residue map for bounded harmonic cocycles. Moreover, we show that the existence of the needed boundary distributions follows from a non-criticality statement for a new class of automorphic forms. We prove a control theorem that implies this non-criticality statement for trivial coefficients. Finally, we apply our constructions to relate spaces of Drinfeld cusp forms for certain congruence subgroups of GL3 and spaces of harmonic cocycles extending work of Teitelbaum to GL3.
date: 2021
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/29302/1/thesis_peter_graef.pdf
identifier: DOI:10.11588/heidok.00029302
identifier: urn:nbn:de:bsz:16-heidok-293022
identifier:   Gräf, Peter Mathias  (2021) Boundary Distributions for GL3 over a Local Field and Symmetric Power Coefficients.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/29302/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng