Submitted by huguenin on
Author's comments: There is as yet no text with the title Functoriality and Reciprocity. Begun as preparations for a lecture, the text appearing here was, and remains, a first attempt to come to terms with the two topics of the title, an attempt that is perhaps doomed by its nature and by my years to remain provisional.
Submitted by admin on
Author's comments: This text is provisional from a mathematical point of view, but it may be some time before the obstacles described in the concluding sections are overcome. Serious progress has been made by Ali Altuğ.
Submitted by admin on
Submitted by admin on
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.
Submitted by admin on
Submitted by admin on
Submitted by admin on
Submitted by admin on
Submitted by admin on
Submitted by admin on
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.