The SL(2)-type and base change

The SL(2)-type of any smooth, irreducible and unitarizable representation of GLn 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 preservedu nder the base change with respect to any finite extension. The Klyachko model of a smooth, irreducible and unitarizable representation π of GLn depends only on the SL(2)-type of π. As a consequence we observe that the Klyachko model of π andof its base change are of the same type.