(1) Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, POB 26, Rehovot, 76100, Israel
Abstract:
Let F be either or . Consider the standard embedding and the action of GLn(F) on GLn+1(F) by conjugation. We show that any GLn(F)-invariant distribution on GLn+1(F) is invariant with respect to transposition. We prove that this implies that for any irreducible admissible smooth Fréchet
representations π of GLn+1(F) and of GLn(F),
. For p-adic fields those results were proven in AGRS].