Lowest weight representations of super Schrodinger algebras in low dimensional spacetime

TL;DR

This paper classifies irreducible lowest weight representations of super Schrödinger algebras in low-dimensional spacetimes, extending the understanding of their structure using explicit singular vector constructions.

Contribution

It provides a systematic classification of irreducible Verma modules for super Schrödinger algebras in (1+1) and (2+1) dimensions with N=1,2 extensions, using a method analogous to semisimple Lie algebras.

Findings

Explicit construction of singular vectors in Verma modules

Classification of irreducible modules in low dimensions

Extension to N=1,2 supersymmetric cases

Abstract

We investigate the lowest weight representations of the super Schrodinger algebras introduced by Duval and Horvathy. This is done by the same procedure as the semisimple Lie algebras. Namely, all singular vectors within the Verma modules are constructed explicitly then irreducibility of the associated quotient modules is studied again by the use of singular vectors. We present the classification of irreducible Verma modules for the super Schrodinger algebras in (1+1) and (2+1) dimensional spacetime with N = 1, 2 extensions.