2010/08/09 by Avraham Aizenbud, Dmitry Gourevitch, Stephen Rallis +1 · 4 citations
Mathematics · #Advanced Algebra and Geometry #Finite Group Theory Research #Advanced Operator Algebra Research #Mathematics #Multiplicity (mathematics) #Invariant (physics) #Unitary state #Pure mathematics #Irreducible representation #Combinatorics #Mathematical analysis #Mathematical physics
paper · pdf · doi:10.4007/annals.2010.172.1413
openalex publication_date 2010/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/22
In the local, characteristic 0, non-Archimedean case, we consider distributions on GL.n C 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 C 1/ to GL.n/. Similar theorems are obtained for orthogonal or unitary groups.