Representations of the Schr\"{o}dinger-Virasoro algebras

TL;DR

This paper classifies irreducible weight modules with finite-dimensional weight spaces over Schr"{o}dinger-Virasoro algebras, showing they are either highest/lowest weight or uniformly bounded, and fully characterizes intermediate series modules.

Contribution

It provides a complete classification of irreducible weight modules and intermediate series modules over Schr"{o}dinger-Virasoro algebras, extending understanding of their representation theory.

Findings

Irreducible weight modules are highest/lowest weight or uniformly bounded.

Complete determination of indecomposable modules of the intermediate series.

Classification results contribute to the representation theory of Schr"{o}dinger-Virasoro algebras.

Abstract

In this paper it is proved that an irreducible weight module with finite-dimensional weight spaces over the Schr\"{o}dinger-Virasoro algebras is a highest/lowest weight module or a uniformly bounded module. Furthermore, indecomposable modules of the intermediate series over these algebras are completely determined.