A proof of the multiplicity one conjecture for GL(n) in GL(n+1)

Details A proof of the multiplicity one conjecture for GL(n) in GL(n+1) A proof of the multiplicity one conjecture for GL(n) in GL(n+1)

2007-07-16

arxiv.org/abs/0707.2363v2

Mathematics

Representation Theory

12 pages. v2: self-contained version

Scientific paper

Let F be a non-archimedean local field of characteristic zero. We consider distributions on GL(n+1,F) which are invariant under the adjoint action of GL(n,F). We prove that any such distribution is invariant with respect to transposition. This implies that the restriction to GL(n) of any irreducible smooth representation of GL(n+1) is multiplicity free. Our paper is based on the recent work [RS] of Steve Rallis and Gerard Schiffmann where they made a remarkable progress on this problem. In [RS], they also show that our result implies multiplicity one theorem for restrictions from the orthogonal group $O(V \oplus F)$ to $O(V)$.

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