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

Abstract

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