2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/160909In this paper we prove that the symmetric pair $(GL_{n+k}(F),GL_n(F) \times GL_k(F))$ is a Gelfand pair for any local field F of characteristic 0. For non-archimedean F it has been proven in [JR]. We use techniques developed in [AG2] to generalize their proof to general local fields.6 pages. v2,v3: minor changesRepresentation Theory20C99; 20G05; 20G25;22E45text