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CATEGORIES:Junior Algebra and Number Theory seminar
SUMMARY:Quantum D-Modules - Nicolas DuprÃ©\, University of
Cambridge
DTSTART;TZID=Europe/London:20150529T150000
DTEND;TZID=Europe/London:20150529T160000
UID:TALK59668AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/59668
DESCRIPTION:In their 2006 paper\, Backelin and Kremnizer devel
oped a theory of quantum D-modules. There had been
several earlier attempts at defining quantum D-mo
dules (e.g. by Tanisaki)\, but they were all tryin
g to define an algebra of quantum differential ope
rators on G/N\, which lead to difficulties. The ap
proach taken by Backelin and Kremnizer was to use
the language of equivariant sheaves\, which allowe
d them to write all the classical definitions they
needed in terms of affine varieties\, i.e. purely
in terms of algebras. For instance\, this allowed
them to define a notion of quantum flag variety.
My aim is to explain their theory of quantum D-mod
ules\, leading to a quantum analogue of the Beilin
son-Bernstein theorem. I will not assume any previ
ous knowledge of quantum groups. Time permitting\,
I will also say something about how one might try
to define quantum p-adic groups.
LOCATION:CMS\, MR14
CONTACT:Julian Brough
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