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SUMMARY:Arthur's multiplicity formula for automorphic representations of c
 ertain inner forms of special orthogonal and symplectic groups - Olivier T
 aïbi (Imperial College)
DTSTART:20151110T141500Z
DTEND:20151110T151500Z
UID:TALK61450@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:I will explain the formulation and proof of Arthur's\nmultipli
 city formula for automorphic representations of certain special\northogona
 l groups and certain inner forms of symplectic groups G over a\nnumber fie
 ld F. I work under an assumption that substantially simplifies\nthe use of
  the stabilisation of the trace formula\, namely that there\nexists a non-
 empty set S of real places of F such that G has discrete\nseries at places
  in S and is quasi-split at places outside S\, and\nby restricting to auto
 morphic representations of G(A_F) which have\nalgebraic regular infinitesi
 mal character at all places in S. In\nparticular\, I prove the general mul
 tiplicity formula for groups G\nsuch that F is totally real\, G is compact
  at all real places of F and\nquasi-split at all finite places of F. Cruci
 ally\, the formulation of\nArthur's multiplicity formula is made possible 
 by Kaletha's recent work\non local and global Galois gerbes and their appl
 ication to the\nnormalisation of Kottwitz-Langlands-Shelstad transfer fact
 ors.
LOCATION:MR13
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