W-superalgebras as truncation of super-Yangians

Abstract

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.

Latex, 32 pages

References in corpus (1)

• Twisted Yangians and folded W-algebras

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• Parabolic presentations of the super Yangian $Y({\mathfrak{gl}}_{M|N})$ associated with arbitrary 01-sequences
• On the finite $W$-algebra for the Lie superalgebra Q(N) in the non-regular case
• Coproduct for affine Yangians and parabolic induction for rectangular $W$-algebras