Invariant distributions on non-distinguished nilpotent orbits with application to the Gelfand property of (GL(2n,R),Sp(2n,R))
| dc.creator | Aizenbud, Avraham | |
| dc.creator | Sayag, Eitan | |
| dc.date | 2008-10-10 | |
| dc.date.accessioned | 2026-07-07T10:09:09Z | |
| dc.date.available | 2026-07-07T10:09:09Z | |
| dc.description | We study invariant distributions on the tangent space to a symmetric space. We prove that an invariant distribution with the property that both its support and the support of its Fourier transform are contained in the set of non-distinguished nilpotent orbits, must vanish. We deduce, using recent developments in the theory of invariant distributions on symmetric spaces that the symmetric pair (GL(2n,R),Sp(2n,R)) is a Gelfand pair. More precisely, we show that for any irreducible smooth admissible Frechet representation $(π,E)$ of GL(2n,R) the space of continuous functionals $Hom_{Sp_{2n}(R)}(E,C)$ is at most one dimensional. Such a result was previously proven for p-adic fields in [HR] for the field of complex numbers in [S]. | |
| dc.description | 11 pages | |
| dc.identifier | https://arxiv.org/abs/0810.1853 | |
| dc.identifier | http://arxiv.org/abs/0810.1853 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/171233 | |
| dc.subject | Representation Theory | |
| dc.subject | 20G05, 22E45, 20C99, 46F10 | |
| dc.title | Invariant distributions on non-distinguished nilpotent orbits with application to the Gelfand property of (GL(2n,R),Sp(2n,R)) | |
| dc.type | text |