  We study the algebraic framework in which one can define, in the manner of
the theta correspondence, a correspondence between representations of two
locally profinite groups $H_1$, $H_2$. In particular, we examine when and how
such a correspondence can be extended to bigger groups $G_1$, $G_2$ containing
$H_1$, $H_2$ respectively as normal subgroups. As an application, we discuss
the theta correspondence for a reductive dual pair of the similitude groups in
the non-archimedean case.
