Multiplicity one Theorems
By Avraham Aizenbud, D. Gourevitch, S. Rallis, G. Schiffmann. 2007
309 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/1b0bb6a5d2bb17964dac3cad7bbfa22f96596c1e
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In Applied Mathematics
- Wei Zhang
- W. Gan
- Akshay Venkatesh
- Atsushi Ichino
- T. Oshima
- Toshiyuki Kobayashi
- Nicolas Bergeron
- Binyong Sun
In Mathematical Physics
- Wei Zhang
- W. Gan
- Atsushi Ichino
- Akshay Venkatesh
- Nicolas Bergeron
- Binyong Sun
- Toshiyuki Kobayashi
- Mehmet Haluk Sengun
Citations in the corpus
- Automorphic period and the central value of Rankin--Selberg L-function (2012, unknown): “First of all, by the multiplicity one result [1],[38], we know a priori that there is a constant denoted by Cπ depending on π such that for all decomposable φ, φ ∈ π, P(φ)P(φ) = Cπ ∏”
- Generic transfer from GSp(4) to GL(4) (2004, unknown): “therefore, by strong multiplicity one theorem [8, 7, 17] we have Π ≃ Π̃ ⊗ ω.”
- Finite multiplicity theorems for induction and restriction (2011, methodology): “Our approach here is based on the theory of systems of partial differential equations with regular singularities, and is completely different from [1, 30] which is based on the Gelfand–Kazhdan criterion.”
- The Gross–Prasad conjecture and local theta correspondence (2014, result): “By surprisingly recent results of Aizenbud-Gourevitch-Rallis-Schiffmann [1] and Sun [17], it is known that the above Hom spaces have dimension at most 1.”
- Fourier transform and the global Gan–Gross–Prasad conjecture for unitary groups (2014, background): “By the multiplicity-one result of [3] and [48], we have dim HomHvpπv,Cq ď 1.”