Singular vectors, characters, and composition series for the N=1 BMS superalgebra

TL;DR

This paper thoroughly analyzes the structure of Verma modules over the N=1 BMS superalgebra, classifying singular vectors and deriving character formulas, thereby advancing understanding of its representation theory.

Contribution

It provides a comprehensive classification of singular and subsingular vectors, and explicitly determines the composition series for the N=1 BMS superalgebra, which was previously unexplored.

Findings

Classification of singular vectors and subsingular vectors

Explicit composition series of Verma modules

Character formulas for irreducible modules

Abstract

This paper investigates the structure of Verma modules over the N=1 BMS superalgebra. We provide a detailed classification of singular vectors, establish necessary and sufficient conditions for the existence of subsingular vectors, uncover the structure of maximal submodules, present the composition series of Verma modules, and derive character formulas for irreducible highest weight modules. As a byproduct, we also explicitly determine all singular vectors, subsingular vectors, and the composition series of Verma modules over the algebra W(2,2).