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CATEGORIES:Number Theory Seminar
SUMMARY:Arthur's multiplicity formula for automorphic repr
esentations of certain inner forms of special orth
ogonal and symplectic groups - Olivier Taïbi (Impe
rial College)
DTSTART;TZID=Europe/London:20151110T141500
DTEND;TZID=Europe/London:20151110T151500
UID:TALK61450AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/61450
DESCRIPTION:I will explain the formulation and proof of Arthur
's\nmultiplicity formula for automorphic represent
ations of certain special\northogonal groups and c
ertain inner forms of symplectic groups G over a\n
number field F. I work under an assumption that su
bstantially simplifies\nthe use of the stabilisati
on of the trace formula\, namely that there\nexist
s 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 t
o automorphic representations of G(A_F) which have
\nalgebraic regular infinitesimal character at all
places in S. In\nparticular\, I prove the general
multiplicity 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. Cru
cially\, 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-Langland
s-Shelstad transfer factors.
LOCATION:MR13
CONTACT:Jack Thorne
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