# Simple bounded highest weight modules of basic classical Lie superalgebras

## TL;DR

This paper classifies all simple bounded highest weight modules of basic classical Lie superalgebras, providing a comprehensive understanding of their structure and character formulas for certain modules.

## Contribution

It offers the first complete classification of simple bounded highest weight modules for basic classical Lie superalgebras and derives character formulas for strongly typical modules.

## Key findings

- Complete classification of simple bounded highest weight modules
- Character formulas for strongly typical modules
- Classification of simple weight modules with finite multiplicities

## Abstract

We classify all simple bounded highest weight modules of a basic classical Lie superalgebra $\mathfrak g$. In particular, our classification leads to the classification of the simple weight modules with finite weight multiplicities over all classical Lie superalgebras. We also obtain some character formulas of strongly typical bounded highest weight modules of $\mathfrak g$.