Multiplicity one Theorems
Representation Theory
2010-11-30 v1
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 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.
Cite
@article{arxiv.0709.4215,
title = {Multiplicity one Theorems},
author = {Avraham Aizenbud and Dmitry Gourevitch and Steve Rallis and Gérard Schiffmann},
journal= {arXiv preprint arXiv:0709.4215},
year = {2010}
}
Comments
A synthesis, with some simplified proofs, of arXiv:0705.2168v1 and arXiv:0707.2363v2