Classification of simple weight modules with finite-dimensional weight spaces over the Schrödinger algebra

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