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SUMMARY:The Drinfeld Upper Half Plane and Smooth Representations of GL2(O_
 F) - Tom Adams\, University of Cambridge
DTSTART:20240508T153000Z
DTEND:20240508T163000Z
UID:TALK216331@talks.cam.ac.uk
CONTACT:Adam Jones
DESCRIPTION:Let F be a finite extension of the p-adic numbers with valuati
 on ring O_F. The Drinfeld upper half plane is a non-archimedean analogue o
 f the complex upper half plane. It is equipped with a natural action of GL
 2(F) and has become ubiquitous in the study of the representation theory o
 f this group. After introducing this space\, in this talk I will use Delig
 ne-Lusztig theory to motivate why we might expect studying equivariant vec
 tor bundles with connection on affinoid subdomains of the Drinfeld upper h
 alf plane to be helpful for exhibiting p-adic geometric realisations of th
 e irreducible\, smooth (complex) representations of GL2(O_F). I will then 
 outline some recent work to this end\, with a focus on some concrete examp
 les.
LOCATION:MR12
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