(GL(n+1,F),GL(n,F)) is a Gelfand pair for any local field F
| dc.creator | Aizenbud, Avraham | |
| dc.creator | Gourevitch, Dmitry | |
| dc.creator | Sayag, Eitan | |
| dc.date | 2007-09-09 | |
| dc.date | 2009-05-17 | |
| dc.date.accessioned | 2026-07-07T13:15:14Z | |
| dc.date.available | 2026-07-07T13:15:14Z | |
| dc.description | Let F be an arbitrary local field. Consider the standard embedding of GL(n,F) into GL(n+1,F) and the two-sided action of GL(n,F) \times GL(n,F) on GL(n+1,F). In this paper we show that any GL(n,F) \times GL(n,F)-invariant distribution on GL(n+1,F) is invariant with respect to transposition. We show that this implies that the pair (GL(n+1,F),GL(n,F)) is a Gelfand pair. Namely, for any irreducible admissible representation $(π,E)$ of (GL(n+1,F), $$dimHom_{GL(n,F)}(E,\cc) \leq 1.$$ For the proof in the archimedean case we develop several new tools to study invariant distributions on smooth manifolds. | |
| dc.description | v3: Archimedean Localization principle excluded due to a gap in its proof. Another version of Localization principle can be found in arXiv:0803.3395v2 [RT]. v4: an inaccuracy with Bruhat filtration fixed. See Theorem 4.2.1 and Appendix B | |
| dc.identifier | https://arxiv.org/abs/0709.1273 | |
| dc.identifier | http://arxiv.org/abs/0709.1273 | |
| dc.identifier | Compositio Mathematica, Volume 144, pp 1504-1524 November 2008 | |
| dc.identifier | doi:10.1112/S0010437X08003746 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/230413 | |
| dc.subject | Representation Theory | |
| dc.subject | 22E,22E45,20G05,20G25,46F99 | |
| dc.title | (GL(n+1,F),GL(n,F)) is a Gelfand pair for any local field F | |
| dc.type | text |