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SUMMARY:Jeffrey Adams (University of Maryland)
DTSTART:20220908T143000Z
DTEND:20220908T160000Z
DTSTAMP:20260422T150025Z
UID:atlas/36
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/atlas/36/">C
 ohomological Arthur packets</a>\nby Jeffrey Adams (University of Maryland)
  as part of Real reductive groups/atlas\n\n\nAbstract\nAn important specia
 l case of Arthur packets are those of regular integral infinitesimal chara
 cter. The trivial representation (attached to the dual principal nilpotent
  orbit) is an example. \n\nIt is known by a result of Salamanca that the u
 nitary representations with regular integral infinitesimal character are p
 recisely the cohomological representations. These are representations with
  non-trivial twisted $(\\mathfrak g\,K)$ cohomology. By a result of Vogan 
 and Zuckerman these are precisely the modules $A_\\mathfrak q(\\lambda)$\,
  constructed via cohomological induction from a unitary character of theta
 -stable Levi subgroup. \n\nThe conclusion is: assuming all is right with t
 he world (i.e. Arthur's conjectures) an Arthur packet consisting of repres
 entations with regular integral infinitesimal character\nmust consist of c
 ertain $A_\\mathfrak q(\\lambda)$-modules. These are sometimes referred to
  as "Adams-Johnson" packets\; these were among the first interesting Arthu
 r packets to be studied in the 1980s.\n\nI'll discuss these things in the 
 context of Atlas.\n
LOCATION:https://researchseminars.org/talk/atlas/36/
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