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SUMMARY:Tensor categories of classical Lie type - Makoto Yamashita (Univer
 sitetet i Oslo)
DTSTART:20230626T101500Z
DTEND:20230626T111500Z
UID:TALK201967@talks.cam.ac.uk
DESCRIPTION:Representation theory of simple Lie groups has interesting def
 ormations in the framework of tensor categories. What kind of categories c
 an have the fusion rules of type A theory (corresponding to finite-dimensi
 onal representations of special linear groups) is well understood by the w
 ork of Kazhdan and Wenzl (1993). We look at the remaining classical series
 \, namely the fusion rules of type BCD theories (corresponding to orthogon
 al and symplectic groups)\, and give a similar classification. The proof i
 s based on Liu&rsquo\;s technique to find Kauffman bracket relations in pl
 anar algebras\, and certain torsion freeness of the Lie type categories by
  Voigt and Goffeng for compact quantum groups\, and by Schopieray and Gann
 on for modular categories. This\, combined with our previous work on the c
 lassification of dimension-preserving fiber functors and categorical Poiss
 on boundary\, leads to a classification of non-Kac type compact quantum gr
 oups of the classical fusion type. Based on ongoing joint work with P. Gro
 ssman and S. Neshveyev.
LOCATION:Seminar Room 1\, Newton Institute
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