Avraham Aizenbud, Dmitry Gourevitch, Steve Rallis, Gérard Schiffmann
Published 2007-09-26Version 1
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.
Comments: A synthesis, with some simplified proofs, of arXiv:0705.2168v1 and arXiv:0707.2363v2
Journal: Annals of Mathematics, Vol. 172 (2010), No. 2, 1407-1434
Local newforms and spherical characters for unitary groups
Multiplicity upon restriction to the derived subgroup
Limit Multiplicity For Unitary Groups and The Stable Trace Formula
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