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SUMMARY:Xuhua He (Chinese U. Hong Kong)
DTSTART:20211006T140000Z
DTEND:20211006T150000Z
DTSTAMP:20260423T035408Z
UID:MITLie/37
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/37/">
 Frobenius-twisted conjugacy classes of loop groups and Demazure product of
  Iwhaori-Weyl groups</a>\nby Xuhua He (Chinese U. Hong Kong) as part of MI
 T Lie groups seminar\n\nLecture held in 2-142.\n\nAbstract\nThe affine Del
 igne-Lusztig varieties\, roughly speaking\,\ndescribe the intersection of 
 Iwahori-double cosets and Frobenius-twisted\nconjugacy classes in a loop g
 roup. For each fixed Iwahori-double coset\n$I w I$\, there exists a unique
  Frobenius-twisted conjugacy class whose\nintersection with $I w I$ is ope
 n dense in $I w I$. Such\nFrobenius-twisted conjugacy class $[b_w]$ is cal
 led the generic\nFrobenius-twisted conjugacy class with respect to the ele
 ment $w$.\nUnderstanding $[b_w]$ leads to some important consequences in t
 he study\nof affine Deligne-Lusztig varieties. In this talk\, I will give 
 an\nexplicit description of $[b_w]$ in terms of Demazure product of the\nI
 wahori-Weyl groups. It is worth pointing out that a priori\, $[b_w]$ is\nr
 elated to the conjugation action on $I w I$\, and it is interesting that\n
 $[b_w]$ can be described using Demazure product instead of conjugation\nac
 tion. This is based on my preprint arXiv:2107.14461.\n\nIf time allows\, I
  will also discuss an interesting application. Lusztig\nand Vogan recently
  introduced a map from the set of translations to the\nset of dominant tra
 nslations in the Iwahori-Weyl group. As an\napplication of the connection 
 between $[b_w]$ and Demazure product\, we\nwill give an explicit formula f
 or the map of Lusztig and Vogan.\n
LOCATION:https://researchseminars.org/talk/MITLie/37/
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