Level-raising and symmetric power functoriality, I

As the simplest case of Langlands functoriality, one expects the existence of the symmetric power S^n of an automorphic representation of GL(2,A) and A denotes the adeles of a number field F. This should be an automorphic representation of GL(N,A) (N = n+1). We show how to deduce, for classical forms, the general case from a recent result of J.T. on deformation theory for "Schur representations", combined with expected results on level-raising, as well as another case (a particular tensor product) of Langlands functoriality.