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Abstract In this paper, we introduce a class of super Adler-type operators associated with the Lie superalgebra gl (m|n) gl (m | n). We show that these operators generate Poisson vertex superalgebras which are isomorphic to the classical W W -superalgebras associated with gl (m|n) gl (m | n) and some rectangular nilpotent elements. We use this isomorphism to construct integrable hierarchies on these rectangular W W -superalgebras.
Carpentier et al. (Mon,) studied this question.
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