Lowest Weight Representations of Super Schrodinger Algebras in One Dimensional Space

TL;DR

This paper studies the structure of lowest weight modules over super Schrodinger algebras in one-dimensional space, classifying irreducible modules and analyzing their reducibility through singular vectors.

Contribution

It provides a detailed classification of irreducible lowest weight modules for N=1,2 super Schrodinger algebras, including explicit reducibility criteria and vector field realizations.

Findings

Classification of irreducible modules for both massive and massless cases

Explicit construction of singular vectors for reducibility analysis

Vector field realizations of the super Schrodinger algebras

Abstract

Lowest weight modules, in particular, Verma modules over the N = 1,2 super Schrodinger algebras in (1+1) dimensional spacetime are investigated. The reducibility of the Verma modules is analyzed via explicitly constructed singular vectors. The classification of the irreducible lowest weight modules is given for both massive and massless representations. A vector field realization of the N = 1, 2 super Schrodinger algebras is also presented.