a1 Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, POB 26, Rehovot 76100, Israel (email: firstname.lastname@example.org)
a2 Faculty of Mathematics and Computer Science, The Weizmann Institute of Science, POB 26, Rehovot 76100, Israel (email: email@example.com)
a3 Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel (email: firstname.lastname@example.org)
Let F be an arbitrary local field. Consider the standard embedding and the two-sided action of GLn(F)×GLn(F) on GLn+1(F). In this paper we show that any GLn(F)×GLn(F)-invariant distribution on GLn+1(F) is invariant with respect to transposition. We show that this implies that the pair (GLn+1(F), GLn(F)) is a Gelfand pair. Namely, for any irreducible admissible representation (π,E) of GLn+1(F), . For the proof in the archimedean case, we develop several tools to study invariant distributions on smooth manifolds.
(Received October 22 2007)
(Accepted May 26 2008)
2000 Mathematics Subject Classification