Robert P. Langlands

Author's comments: It is likely that these two letters to Serge Lang, like my earlier letter to Weil on problems in the theory of automorphic forms, were never read with any attention by the recipient. Moreover, the earlier letter is a model of clarity compared with these two. Besides, there is, in retrospect, no reason to think that either Lang or Weil had the necessary background in the theory of semisimple groups and certainly not in the theory of their infinite-dimensional representations.

Author's comments: The Galois representations attached in the context of Shimura varieties to certain automorphic representations usually correspond---under the correspondence of the "Langlands program"---not to the representation to which they are attached but to some twist of it by a central character. There is no reason---logical or aesthetical---that it should be otherwise. Nevertheless a casual search of the literature will probably reveal that a number of authors were troubled by it and attempted---on their own initiative---to revise the definitions.