Math

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.