2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/167705The SL(2)-type of any smooth, irreducible and unitarizable representation of GL(n) over a p-adic field was defined by Venkatesh. We provide a natural way to extend the definition to all smooth and irreducible representations. For unitarizable representations we show that the SL(2)-type of a representation is preserved under base change with respect to any finite extension. The Klyachko model of a smooth, irreducible and unitarizable representation πof GL(n) depends only on the SL(2)-type of π. As a consequence we observe that the Klyachko model of πand of its base-change are of the same type.10 pagesNumber TheoryRepresentation Theorytext