nLab Langlands dual group


See at Langlands correspondence.


Remark on terminology: Robert Langlands did not actually introduce or use the term “dual group”. The original texts just speak of the “L-group” (Gelbhart 84, page 29 (205)). Also, the role of LG{}^L G in the number-theoretic Langlands program is not as symmetric as in the geometric Langlands program, it essentially serves as an ingredient for the construction of automorphic L-functions from Galois representations in GG. In the comment to a message to Sarnak (2014) Langlands writes:

This duality [[ electric-magnetic duality/S-duality ]] is quite different than the functoriality and reciprocity introduced in the arithmetic theory [[ of the Langlands program ]].

Further comments along these lines are in (Langlands 14, pages 6-7).


Last revised on September 7, 2014 at 09:19:07. See the history of this page for a list of all contributions to it.