Level-raising and symmetric power functoriality, I

Laurent Clozel (1) , Jack A. Thorne (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 Harvard University - Department of Mathematics

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.

Keywords: modular forms; principe de fonctorialité.

Keywords: principe de fonctorialité

Domains: Number Theory [math.NT]

Laurent Clozel, Jack A. Thorne. Level-raising and symmetric power functoriality, I. 2013. ⟨hal-00957981⟩