(GL(2n,C),SP(2n,C)) is a Gelfand Pair

dc.creatorSayag, Eitan
dc.date2008-05-19
dc.date.accessioned2026-07-07T09:39:34Z
dc.date.available2026-07-07T09:39:34Z
dc.descriptionWe 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.description10 pages
dc.identifierhttps://arxiv.org/abs/0805.2625
dc.identifierhttp://arxiv.org/abs/0805.2625
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161219
dc.subjectRepresentation Theory
dc.subjectNumber Theory
dc.subject22E,22E45,20G05,20G25,46F99
dc.title(GL(2n,C),SP(2n,C)) is a Gelfand Pair
dc.typetext

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