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SUMMARY:Lucas Mason-Brown (University of Oxford)
DTSTART:20230427T150000Z
DTEND:20230427T160000Z
DTSTAMP:20260404T094801Z
UID:FCGRepresentationTheorySeminars/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/FCGRe
 presentationTheorySeminars/1/">Endoscopic lifting and cohomological induct
 ion</a>\nby Lucas Mason-Brown (University of Oxford) as part of Feza Gurse
 y Center Representation Theory Seminars\n\n\nAbstract\nLet $G$ and $H$ be 
 real reductive groups. To any $L$-homomorphism $e:{}^LH\\rightarrow {}^LG$
  one can associate a map $e_∗$ from virtual representations of $H$ to vi
 rtual representations of $G$. This map was predicted by Langlands and defi
 ned (in the real case) by Adams\, Barbasch\, and Vogan. Without further re
 strictions on $e$\, this map can be very poorly behaved. A special case in
  which $e_∗$ exhibits especially nice behavior is the case when $H$ is a
 n endoscopic group. In this talk\, I will introduce a more general class o
 f $L$-homomorphisms which exhibit similar behavior to the endoscopic case.
  I will explain how this more general notion of endoscopic lifting relates
  to the theory of cohomological induction. I will also explain how this ge
 neralized notion of endoscopic lifting can be used to prove the unitarity 
 of many Arthur packets. This is based on joint work with Jeffrey Adams and
  David Vogan.\n
LOCATION:https://stable.researchseminars.org/talk/FCGRepresentationTheoryS
 eminars/1/
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