On the notion of the parabolic and the cuspidal support of smooth-automorphic forms and smooth-automorphic representations (Q6565879)

Let \(G\) stand for a general connected reductive group over a number field. In the paper under the review, the authors study smooth-automorphic forms on \(G\) and the internal structure of the representation theory of Franke's space in the smooth-automorphic framework.\N\NThe authors show that the decompositions along the parabolic support and along the cuspidal support transfer in a topologized version of the limit-Frechet space of smooth-automorphic forms. A concise treatment of the theory of space of smooth-automorphic forms from the topological point of view is also provided.