Multiplicity one theorem for $(\mathrm{GL}_{n+1},\mathrm{GL}_n)$ over a local field of positive characteristic
Abstract
Let $\mathbb{F}$ be a nonarchimedean local field of positive characteristic different from 2. We consider distributions on $\mathrm{GL}(n+1,\mathbb{F})$ which are invariant under the adjoint action of $\mathrm{GL}(n,\mathbb{F})$. We prove that any such distribution is invariant with respect to transposition. This implies that the restriction to $\mathrm{GL}(n,\mathbb{F})$ of any irreducible smooth representation of $\mathrm{GL}(n+1,\mathbb{F})$ is multiplicity free.
 Publication:

arXiv eprints
 Pub Date:
 May 2019
 arXiv:
 arXiv:1905.01321
 Bibcode:
 2019arXiv190501321M
 Keywords:

 Mathematics  Representation Theory;
 22E50 (Primary) 20G05;
 20G25;
 46F10 (Secondary)
 EPrint:
 This article draws heavily from arXiv:0707.2363 by other author