In mathematics, the Langlands group is a conjectural
group ''L''
''F'' attached to each local or global field ''F'', that satisfies properties similar to those of the
Weil group. It was given that name by
Robert Kottwitz
Robert Edward Kottwitz (born 1950 in Lynn, Massachusetts) is an American mathematician.
Kottwitz studied at the University of Washington (B.A.) and then went to Harvard University, where he received his Ph.D. in 1977 under the supervision of Phil ...
. In Kottwitz's formulation, the Langlands group should be an extension of the Weil group by a compact group. When ''F'' is local archimedean, ''L
F'' is the Weil group of ''F'', when ''F'' is local non-archimedean, ''L
F'' is the product of the Weil group of ''F'' with SU(2). When ''F'' is global, the existence of ''L
F'' is still conjectural, though James Arthur gives a conjectural description of it. The Langlands correspondence for ''F'' is a "natural" correspondence between the irreducible ''n''-dimensional complex representations of ''L
F'' and, in the local case, the cuspidal automorphic representations of GL
''n''(A
''F''), where A
''F'' denotes the
adele
Adele Laurie Blue Adkins (, ; born 5 May 1988), professionally known by the mononym Adele, is an English singer and songwriter. After graduating in arts from the BRIT School in 2006, Adele signed a reco ...
s of ''F''.
Notes
References
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*
*{{citation, mr=0546619
, last=Langlands, first= R. P.
, chapter=Automorphic representations, Shimura varieties, and motives. Ein Märchen, title= Automorphic forms, representations and L-functions , series=Proc. Sympos. Pure Math., pages= 205–246, volume=33, isbn=978-0-8218-1437-6 , date=1979-06-30
Langlands program