(GL(2n,C),SP(2n,C)) is a Gelfand Pair
| dc.creator | Sayag, Eitan | |
| dc.date | 2008-05-19 | |
| dc.date.accessioned | 2026-07-07T09:39:34Z | |
| dc.date.available | 2026-07-07T09:39:34Z | |
| dc.description | We prove that (GL_{2n}(C),Sp_{2n}(C)) is a Gelfand pair. More precisely, we show that for an irreducible smooth admissible Frechet representation (π,E) of GL_{2n}(C) the space of continuous functionals Hom_{Sp_{2n}(\cc)}(E,C) is at most one dimensional. For this we show that any distribution on GL_{2n}(C) invariant with respect to the double action Sp_{2n}(C) \times Sp_{2n}(C) is transposition invariant. Such a result was previously proven for p-adic fields by M. Heumos and S. Rallis. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/0805.2625 | |
| dc.identifier | http://arxiv.org/abs/0805.2625 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/161219 | |
| dc.subject | Representation Theory | |
| dc.subject | Number Theory | |
| dc.subject | 22E,22E45,20G05,20G25,46F99 | |
| dc.title | (GL(2n,C),SP(2n,C)) is a Gelfand Pair | |
| dc.type | text |