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

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.