  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
that an admissible irreducible representation of GL(n+1), when restricted to
GL(n) decomposes with multiplicity one.
  Similar Theorems are obtained for orthogonal or unitary groups.

Representation Theory