The paper claims the Macdonald correspondence is uniquely characterized by central character and pair epsilon-factors, but the proof of this characterization is incomplete.
Deligne, ``Les constantes des \'equations fonctionnelles des functions L ", in Modular functions of one variable, II, Lecture Notes in Math
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On the Macdonald correspondence
The paper claims the Macdonald correspondence is uniquely characterized by central character and pair epsilon-factors, but the proof of this characterization is incomplete.