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SUMMARY:Hans Wenzl (UCSD)
DTSTART:20210608T183000Z
DTEND:20210608T191500Z
DTSTAMP:20260423T004516Z
UID:Opalg21/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/Opalg21/4/">
 Subfactors\, Tensor Categories and Module Categories</a>\nby Hans Wenzl (U
 CSD) as part of Conference on operator algebras and related topics in Ista
 nbul\, 2021\n\n\nAbstract\nWhen Vaughan Jones started to think about the n
 otion of an index for subfactors\, the only known examples came from group
 s and their representations and from the embedding of groups H < G. In bot
 h cases the indices were integers. Vaughan's surprising examples with non-
 integer index were later connected to representations of the quantum group
  U_q(sl2) and to representations of the loop group LSU(2). This was subseq
 uently generalized to the construction of a sequence of subfactors for eve
 ry representation of a semisimple Lie algebra.The question remains to cons
 truct subfactors corresponding to analogs of subgroups of Lie groups\; in 
 modern language this amounts to classifying module categories of certain t
 ensor categories. Again\, Vaughan made important contributions for solving
  the problem for the sl_2 case constructing what is generally referred to 
 as Goodman-de la Harpe-Jones subfactors. While complete classifications ar
 e known for several Lie groupsof small rank\, the general problem is still
  far from being solved. We give an overview of the current state of knowle
 dge\, and present some explicit examples.\n
LOCATION:https://researchseminars.org/talk/Opalg21/4/
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