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SUMMARY:Geoffrey Janssens (Catholic University of Louvain\, Belgium)
DTSTART:20250505T150000Z
DTEND:20250505T160000Z
DTSTAMP:20260423T021118Z
UID:ENAAS/122
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/ENAAS/122/">
 On the loop Hecke algebra</a>\nby Geoffrey Janssens (Catholic University o
 f Louvain\, Belgium) as part of European Non-Associative Algebra Seminar\n
 \n\nAbstract\nTo any braid group $B_n$ ​ there is an associated (Iwahori
 -)Hecke algebra $H_q ​ (n)$. Over time this algebra has shown to be as i
 ntriguing as $B_n$. For example\, $H_q ​ (n)$ possesses a representation
  for which it is in a Schur–Weyl relation with $U_q ​ (sl_d). One poss
 ible interpretation of classical braid groups is as a fundamental group of
  the space of configurations of $n$ distinct points in  $R^2$. Taking this
  motion group perspective\, it is natural to consider configurations of $n
 $ unit circles $S^1$. This yields the so-called Loop Braid group. Damiani
 –Martin–Rowell associated an analogue of the Hecke algebra and made a 
 conjecture on the dimension of this Loop Hecke algebra. In this talk we wi
 ll firstly briefly introduce the mentioned objects and subsequently tell a
 bout how the above Schur–Weyl picture adapts to the Loop setting. In the
  last part of the talk we will discuss the simple representations and the 
 Jacobson radical.\n
LOCATION:https://researchseminars.org/talk/ENAAS/122/
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