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SUMMARY:Self-dual cuspidal and supercuspidal representations - Jeffrey Adl
 er (American University)
DTSTART:20190521T133000Z
DTEND:20190521T143000Z
UID:TALK123505@talks.cam.ac.uk
CONTACT:Jessica Fintzen
DESCRIPTION:According to the Harish-Chandra philosophy\, cuspidal represen
 tations are the basic building blocks in the representation theory of fini
 te reductive groups.  Similarly for supercuspidal representations of p-adi
 c groups.  Self-dual representations play a special role in the study of p
 arabolic induction.  Thus\, it is of interest to know whether self-dual (s
 uper)cuspidal representations exist.  With a few exceptions involving some
  small fields\, I will show precisely when a finite reductive group has ir
 reducible cuspidal representations that are self-dual\, of Deligne-Lusztig
  type\, or both.  Then I will look at implications for the existence of ir
 reducible\, self-dual supercuspidal representations of p-adic groups.  Thi
 s is joint work with Manish Mishra.
LOCATION:MR13
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