English

Multiplicity one Conjectures

Representation Theory 2007-05-23 v1

Abstract

In the first part, in the local non archimedean case, we consider distributions on GL(n+1) which are invariant under the adjoint action of GL(n). We conjecture that such distributions are invariant by transposition. This would imply multiplicity at most one for restrictions from GL(n+1) to GL(n). We reduce ourselves to distributions with "singular" support and then finish the proof for n< 9. In the second part we show that similar Theorems for orthogonal or unitary groups follow from the case of GL(n)

Keywords

Cite

@article{arxiv.0705.2168,
  title  = {Multiplicity one Conjectures},
  author = {Steve Rallis and Gérard Schiffmann},
  journal= {arXiv preprint arXiv:0705.2168},
  year   = {2007}
}
R2 v1 2026-06-21T08:28:33.472Z