  Based on the differential graded Lie algebra controlling deformations of an
$n$-Lie algebra with a representation (called an n-LieRep pair), we construct a
Lie n-algebra, whose Maurer-Cartan elements characterize relative Rota-Baxter
operators on n-LieRep pairs. The notion of an n-pre-Lie algebra is introduced,
which is the underlying algebraic structure of the relative Rota-Baxter
operator. We give the cohomology of relative Rota-Baxter operators and study
infinitesimal deformations and extensions of order m deformations to order m+1
deformations of relative Rota-Baxter operators through the cohomology groups of
relative Rota-Baxter operators. Moreover, we build the relation between the
cohomology groups of relative Rota-Baxter operators on n-LieRep pairs and those
on (n+1)-LieRep pairs by certain linear functions.
