On polynomial representations of classical strange Lie superalgebras

TL;DR

This paper studies polynomial representations of strange classical Lie superalgebras, revealing indecomposability for type P and a direct sum decomposition into irreducibles for type Q, advancing understanding of their module structures.

Contribution

It provides the first detailed analysis of polynomial modules for these superalgebras, including composition series and irreducible decompositions.

Findings

Type P modules are indecomposable with known composition series.

Type Q modules decompose into a direct sum of irreducible submodules.

Enhanced understanding of the structure of polynomial representations of strange Lie superalgebras.

Abstract

In this paper, various polynomial representations of strange classical Lie superalgebras are investigated. It turns out that the representations for the algebras of type P are indecomposable, and we obtain the composition series of the underlying modules. As modules of the algebras of type Q, the polynomial algebras are decomposed into a direct sum of irreducible submodules.