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SUMMARY:David Vogan (MIT)
DTSTART:20210908T200000Z
DTEND:20210908T210000Z
DTSTAMP:20260423T035407Z
UID:MITLie/33
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MITLie/33/">
 Constructing unipotent representations</a>\nby David Vogan (MIT) as part o
 f MIT Lie groups seminar\n\nLecture held in 2-142.\n\nAbstract\nIn the 195
 0s\, Mackey began a systematic analysis of unitary representations of grou
 ps in terms of "induction" from normal subgroups. Ultimately this led to a
  fairly good reduction of unitary representation theory to the case of sim
 ple groups\, which lack interesting normal subgroups. At about the same ti
 me\, Gelfand and Harish-Chandra understood that many representations of si
 mple groups could be constructed using induction from parabolic subgroups.
  After many refinements and extensions of this work\, there still remain a
  number of interesting representations of simple groups that are often not
  obtained by parabolic induction.\n\nFor the case of real reductive groups
 \, I will discuss a certain (finite) family of representations\, called un
 ipotent\, whose existence was conjectured by Arthur in the 1980s. Some uni
 potent representations can in fact be obtained by parabolic induction\; I 
 will talk about when this ought to happen\, and about the (rather rare) ca
 ses in which Arthur's unipotent representations are not induced. (A lot of
  what I will say is meaningful and interesting over local or finite fields
 \, but I know almost nothing about those cases.)\n
LOCATION:https://researchseminars.org/talk/MITLie/33/
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