Integrable bounded weight modules of classical Lie superalgebras at infinity

TL;DR

This paper classifies integrable bounded simple weight modules over classical Lie superalgebras at infinity, analyzes their categories, and shows that these categories are mostly semisimple, advancing understanding of their structure.

Contribution

It provides a classification of integrable bounded simple weight modules and demonstrates the semisimplicity of their categories for most classical Lie superalgebras at infinity.

Findings

Classification of integrable bounded simple weight modules

Most categories are semisimple

Enhanced understanding of module structures at infinity

Abstract

We classify integrable bounded simple weight modules over classical Lie superalgebras at infinity. We also study the categories of such modules, and we prove that for most of the classical Lie superalgebras at infinity the respective category is semisimple.