Abstract
In this paper, we characterize a relative Rota-Baxter operator on an n-Lie superalgebra with a representation (called an n-LSRep pair) as a Maurer-Cartan element of a certain Lie n-algebra. Then, we introduce the notions of n-pre-Lie superalgebras and symplectic n-Lie superalgebras and give some related results based on relative Rota-Baxter operators. In the next part, we give the cohomologies of relative Rota-Baxter operators on n-LSRep pairs and study infinitesimal deformations and extensions of finite order deformations of relative Rota-Baxter operators through the cohomology groups of relative Rota-Baxter operators. Finally, we build the relationship between the cohomology groups of relative Rota-Baxter operators on n-LSRep pairs and those on ( n + 1 ) -LSRep pairs by certain linear functions.
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