Classification of simple weight modules with finite-dimensional weight spaces over the Schr\"odinger algebra

TL;DR

This paper classifies simple weight modules with finite-dimensional weight spaces over the Schrödinger algebra, using existing module descriptions, twisting functors, and dimension results to provide a comprehensive understanding of these modules.

Contribution

It provides a complete classification of simple weight modules with finite-dimensional weight spaces over the Schrödinger algebra, extending prior module descriptions and applying advanced functor techniques.

Findings

Classification of simple weight modules achieved

Identification of modules with finite-dimensional weight spaces

Application of twisting functors and dimension results

Abstract

We classify simple weight modules with finite-dimensional weight spaces over the (centrally extended complex) Schr\"odinger algebra in (1+1)-dimensional space-time. Our arguments use the description of lowest weight modules by Dobrev, Doebner and Mrugalla; Mathieu's twisting functors and results of Wu and Zhu on dimensions of weight spaces in dense modules.