Abstract :
This paper describes the lifting of automorphic characters of image to image. It does so by matching the image of this lift with the lift of automorphic characters from image to image. Our matching actually gives a matching of individual automorphic forms, and not just of representation spaces. Let V be a 3-dimensional quadratic vector space and U a certain 1-dimensional quadratic space. To an automorphic form IV(χ,φ) determined by the Schwartz function image in the lift of the character χ we match an automorphic form IU(μ,φ0) determined by the Schwartz function image in the lift of the character μ. Our work shows that, the space U is explicitly determined by the character χ. The character μ is explicitly determined by the space V and the function φ0 is given by an orbital integral involving φ.
