Irreducible Continuous Representations of the Simple Linearly Compact n-Lie Superalgebra of type W

TL;DR

This paper classifies all irreducible continuous representations of a specific simple linearly compact n-Lie superalgebra of type W, linking them to representations of a related Lie algebra with a trivial ideal action.

Contribution

It provides the first complete classification of irreducible continuous representations for this class of n-Lie superalgebras, establishing a correspondence with Lie algebra representations.

Findings

Classification of all irreducible continuous representations achieved.

Established a bijective correspondence with Lie algebra representations.

Identified the trivial action of a two-sided ideal in the classification.

Abstract

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 W^n and continuous representations of the Lie algebra of Cartan type W_{n-1}, on which some two-sided ideal acts trivially.