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CATEGORIES:Junior Algebra and Number Theory seminar
SUMMARY:A category O for quantum Arens-Michael envelopes.
- Nicolas Dupré
DTSTART;TZID=Europe/London:20181012T150000
DTEND;TZID=Europe/London:20181012T160000
UID:TALK112444AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/112444
DESCRIPTION:Classically\, the BGG category O of a complex semi
simple Lie algebra is a subcategory of its categor
y of representations which is particularly well-be
haved. It contains all the highest weight modules
and so in particular all the finite dimensional re
presentations\, and it has nice combinatorics (e.g
. BGG reciprocity). There is a natural analogue of
this category for quantum groups\, which more pre
cisely corresponds to the integral category O (i.e
. the direct sum of all the integral blocks). A fe
w years ago\, Tobias Schmidt defined a category O
for the Arens-Michael envelope of the enveloping a
lgebra of a p-adic Lie algebra. This Arens-Michael
envelope can be defined as a certain Fréchet comp
letion of the enveloping algebra\, and it satisfie
s certain properties which makes it what is called
a Fréchet-Stein algebra. These algebras have a ni
ce category of modules\, called coadmissible\, and
Schmidt defined his category O as a certain subca
tegory of the category of all coadmissible modules
. His main result was that his category is equival
ent to the usual category O of the Lie algebra. In
this talk\, we will explain how to construct a qu
antum analogue of the Arens-Michael envelope and a
category O for it. We will then see that the anal
ogue of Schmidt's theorem is also true for our cat
egory.
LOCATION:CMS\, MR14
CONTACT:Richard Freeland
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