W-superalgebras as truncation of super-Yangians

We show that some finite W-superalgebras based on gl(M|N) are truncation of the super-Yangian Y(gl(M|N)). In the same way, we prove that finite W-superalgebras based on osp(M|2n) are truncation of the twisted super-Yangians Y(gl(M|2n))^{+}. Using this homomorphism, we present these W-superalgebras in an R-matrix formalism, and we classify their finite-dimensional irreducible representations.