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SUMMARY:Representations of GL_2(F) and Equivariant Vector Bundles with Con
 nection on the Drinfeld Upper Half-Plane. - James Taylor\, University of O
 xford
DTSTART:20240313T163000Z
DTEND:20240313T173000Z
UID:TALK210865@talks.cam.ac.uk
CONTACT:Adam Jones
DESCRIPTION:If F is a finite extension of Q_p\, then the Drinfeld upper ha
 lf-plane is a certain non-archimedean analogue of the complex upper half p
 lane. This space has a natural action of GL_2(F)\, and has been shown to b
 e a very fruitful object to study if one is interested in the representati
 on theory of GL_2(F). In this talk\, I will introduce this space\, and try
  to motivate why one might be interested in studying equivariant vector bu
 ndle with connection on this space in order to better understand locally a
 nalytic representations of GL_2(F). I will also explain my current work wh
 ich classifies exactly which of these equivariant vector bundles with conn
 ection arise from the Drinfeld tower\, and relates this subcategory to the
  category of smooth representations of the group of norm one elements in D
 \, the central division algebra over F of dimension 4.
LOCATION:MR12
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