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SUMMARY:A category O for quantum Arens-Michael envelopes. - Nicolas Dupré
DTSTART:20181012T140000Z
DTEND:20181012T150000Z
UID:TALK112444@talks.cam.ac.uk
CONTACT:Richard Freeland
DESCRIPTION:Classically\, the BGG category O of a complex semisimple Lie a
 lgebra is a subcategory of its category of representations which is partic
 ularly well-behaved. It contains all the highest weight modules and so in 
 particular all the finite dimensional representations\, and it has nice co
 mbinatorics (e.g. BGG reciprocity). There is a natural analogue of this ca
 tegory for quantum groups\, which more precisely corresponds to the integr
 al category O (i.e. the direct sum of all the integral blocks). A few year
 s ago\, Tobias Schmidt defined a category O for the Arens-Michael envelope
  of the enveloping algebra of a p-adic Lie algebra. This Arens-Michael env
 elope can be defined as a certain Fréchet completion of the enveloping al
 gebra\, and it satisfies certain properties which makes it what is called 
 a Fréchet-Stein algebra. These algebras have a nice category of modules\,
  called coadmissible\, and Schmidt defined his category O as a certain sub
 category of the category of all coadmissible modules. His main result was 
 that his category is equivalent to the usual category O of the Lie algebra
 . In this talk\, we will explain how to construct a quantum analogue of th
 e Arens-Michael envelope and a category O for it. We will then see that th
 e analogue of Schmidt's theorem is also true for our category.
LOCATION:CMS\, MR14
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