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SUMMARY:Simon Lentner (OIST)
DTSTART:20261013T070000Z
DTEND:20261013T080000Z
DTSTAMP:20261006T143521Z
UID:OISTRTS/86
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OISTRTS/86/"
 >Nichols algebras and Kazhdan Lusztig correspondences</a>\nby Simon Lentne
 r (OIST) as part of OIST representation theory seminar\n\n\nAbstract\nTo a
 ny object in a braided tensor category we can associate a Nichols algebra\
 , either through braid group combinatorics or through a universal property
 . The main motiviation for Nichols algebras is to systematically construct
  the quantum group from its Cartan part\, but it can be used to construct 
 many novel braided tensor categories with interesting root system structur
 e. In conformal field theory\, braidings appear as monodromies of certain 
 differential equations such as the Knizhnik–Zamolochikov equation. The K
 azhdan–Lusztig correspondence links the representation theory appearing 
 in such conformal field theories to quantum groups. Using Nichols algebras
  and other categorical tools\, we have recently proven a nonsemisimple ver
 sion of this result conjectured by Feigin et al. In our most recent work\,
  we determine the braided tensor category of modules of affine sl(2) at ad
 missible level in terms of a quantum group of type sl(2|1).\n
LOCATION:https://researchseminars.org/talk/OISTRTS/86/
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