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

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