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SUMMARY:Jones-Temperley-Lieb Algebras from the viewpoint of noncommutative
  probability - Claus Koestler (University College Cork)
DTSTART:20241202T141000Z
DTEND:20241202T143000Z
UID:TALK224629@talks.cam.ac.uk
DESCRIPTION:Thoma's theorem provides a characterization of the extremal ch
 aracters of the infinite symmetric group. Using distributional invariance 
 principles in noncommutative probability\, this famous theorem was shown b
 y Gohm and K&ouml\;stler to form part of a quantum de Finetti theorem. A k
 ey element of the underlying operator algebraic approach was the considera
 tion of the infinite symmetric group presented via star generators. Furthe
 rmore\, Nica and K&ouml\;stler identified that the central limit laws of t
 his sequence of star generators\, with respect to certain extremal charact
 ers\, correspond to the empirical law of traceless GUE random d x d matric
 es.\nMy talk will briefly review these results and address ongoing researc
 h into transferring them to extremal tracial states on the Jones-Temperley
 -Lieb algebras. A successful transfer would highlight the robustness of th
 e Jones index as a consequence of a noncommutative de Finetti theorem.
LOCATION:Seminar Room 1\, Newton Institute
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