Bounded highest weight modules of q(n)

TL;DR

This paper classifies all simple highest weight bounded modules of the queer Lie superalgebra q(n) using a novel combinatorial tool called the star action, also leading to a classification of all simple weight modules.

Contribution

Introduces the star action as a new combinatorial tool for classifying modules of q(n), advancing the understanding of queer Lie superalgebra representations.

Findings

Complete classification of simple highest weight bounded modules of q(n)

Introduction of the star action for combinatorial analysis

Classification of all simple weight q(n)-modules

Abstract

A classification of the simple highest weight bounded modules of the queer Lie superalgebras q(n) is obtained. To achieve this classification we introduce a new combinatorial tool - the star action. Our result leads in particular to a classification of all simple weight q(n)-modules.