  Given a $B$-pair $W$ and a Schur functor $S$, we show under some general
assumptions that $W$ is trianguline if and only if $S(W)$ is. This is an
extension of earlier work of Di Matteo. We derive some consequences on the
behavior of local Galois representations under morphisms of Langlands dual
groups. We attach to a Schur functor a map between the trianguline deformation
spaces defined by Hellmann, and we study congruence loci on the
Hecke-Taylor-Wiles varieties constructed by Breuil, Hellmann and Schraen for
unitary groups.
