Irreducible continuous representations of the simple linearly compact n-Lie superalgebra of type W

In the present paper we classify all irreducible continuous representations of the simple linearly compact n-Lie superalgebra of type W. The classification is based on a bijective correspondence between the continuous representations of the n-Lie algebras Wn and continuous representations of the Lie algebra of Cartan type Wn−1, on which some two-sided ideal acts trivially.