  We prove in some cases a formula for the Greenberg-Benois
$\mathcal{L}$-invariant of the spin, standard and adjoint Galois
representations associated with Siegel-Hilbert modular forms. In order to
simplify the calculation, we give a new definition of the
$\mathcal{L}$-invariant for a Galois representation $V$ of a number field
$F\neq \mathbb{Q}$; we also check that it is compatible with Benois' definition
for $\mathrm{Ind}_F^{\mathbb{Q}}(V)$.
