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CATEGORIES:Junior Algebra and Number Theory seminar
SUMMARY:Towards a Beilinson-Bernstein Theorem for p-adic Q
uantum Groups - Nicolas DuprÃ©\, University of Camb
ridge
DTSTART;TZID=Europe/London:20171201T150000
DTEND;TZID=Europe/London:20171201T160000
UID:TALK86331AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/86331
DESCRIPTION:In 1981\, Beilinson and Bernstein used their celeb
rated localisation theorem to prove the Kazdhan-Lu
sztig conjecture on characters of highest weight m
odules. The theorem established a correspondence b
etween representations of a complex semisimple Lie
algebra and modules over certain sheaves of diffe
rential operators on the flag variety of the assoc
iated algebraic group\, and it is considered as on
e of the starting points of geometric representati
on theory. Since then there have been many general
isations of this result\, as well as analogues of
it in different contexts. For example\, Backelin a
nd Kremnizer proved a localisation theorem for rep
resentations of quantum groups. More recently\, Ar
dakov and Wadsley proved a localisation theorem wo
rking with certain completed enveloping algebras o
f p-adic Lie algebras. In this talk I will explain
what these two specific theorems say and how one
might attempt to combine the ideas involved in the
ir proofs to obtain a localisation theorem for cer
tain p-adic completions of quantum groups.
LOCATION:CMS\, MR14
CONTACT:Nicolas DuprÃ©
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