Multiplicity one theorems

Abstract

In the local, characteristic 0, non-Archimedean case, we consider distributions on GL.(n+1) which are invariant under the adjoint action of GL.(n). We prove that such distributions are invariant by transposition. This implies multiplicity at most one for restrictions from GL.(n+1) to GL.(n). Similar theorems are obtained for orthogonal or unitary groups. © 2010 by Princeton University.