Multiplicity one theorem for (GL_n+1 (R), GL_n(R))
By Avraham Aizenbud, D. Gourevitch. 2008
70 citations recorded by the source corpus.
Let F be either R or C. Consider the standard embedding GLn(F ) ↪→ GLn+1(F ) and the action of GLn(F ) on GLn+1(F ) by conjugation. In this paper we show that any GLn(F )-invariant distribution on GLn+1(F ) is invariant with respect to transposition. We show that this implies that for any irreducible admissible smooth Frechet representations π of GLn+1(F ) and τ of GLn(F ), dim HomGLn(F )(π, τ) ≤ 1. For p-adic fields those results were proven in [AGRS]. Mathematics Subject Classification (2000). 20G05, 22E45, 20C99, 46F10.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/da00f54434ccd80551f0f5c8058fb8b1fc4de48e
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In Algebra and Number Theory
- W. Gan
- Dipendra Prasad
- B. Gross
- Manjul Bhargava
- Wei Zhang
- Atsushi Ichino
- E. Viehmann
- Michael Rapoport
In Geometry and Topology
- W. Gan
- Dipendra Prasad
- B. Gross
- Manjul Bhargava
- Atsushi Ichino
- Hiraku Atobe
- Mark Reeder
- Xiaoheng Wang
In Mathematical Physics
- W. Gan
- Dipendra Prasad
- B. Gross
- Manjul Bhargava
- Atsushi Ichino
- Wei Zhang
- Michael Rapoport
- Hiraku Atobe
Citations in the corpus
- Symplectic local root numbers, central critical L-values, and restriction problems in the representation theory of classical groups (2009, methodology): “h element on the LHS, [JSZ] constructs an associated element on the RHS, using an explicit integral. This is enough to deduce the multiplicity one result of Corollary 15.2from the results of [SZ] and [AG]. 64 WEETECKGAN,BENEDICTH.GROSSANDDIPENDRAPRASAD 16. Uniqueness of Fourier-Jacobi Models In this”