nLab
Langlands dual group

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See at Langlands correspondence.

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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).

References

Revised on September 7, 2014 09:19:07 by David Corfield (91.125.67.210)