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SUMMARY:Towards a Beilinson-Bernstein Theorem for p-adic Quantum Groups - 
 Nicolas Dupré\, University of Cambridge
DTSTART:20171201T150000Z
DTEND:20171201T160000Z
UID:TALK86331@talks.cam.ac.uk
CONTACT:Nicolas Dupré
DESCRIPTION:In 1981\, Beilinson and Bernstein used their celebrated locali
 sation theorem to prove the Kazdhan-Lusztig conjecture on characters of hi
 ghest weight modules. The theorem established a correspondence between rep
 resentations of a complex semisimple Lie algebra and modules over certain 
 sheaves of differential operators on the flag variety of the associated al
 gebraic group\, and it is considered as one of the starting points of geom
 etric representation theory. Since then there have been many generalisatio
 ns of this result\, as well as analogues of it in different contexts. For 
 example\, Backelin and Kremnizer proved a localisation theorem for represe
 ntations of quantum groups. More recently\, Ardakov and Wadsley proved a l
 ocalisation theorem working with certain completed enveloping algebras of 
 p-adic Lie algebras. In this talk I will explain what these two specific t
 heorems say and how one might attempt to combine the ideas involved in the
 ir proofs to obtain a localisation theorem for certain p-adic completions 
 of quantum groups.
LOCATION:CMS\, MR14
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