Abstract
In this paper, we study weight representations over the Schrödinger Lie algebra sn for any positive integer n. It turns out that the algebra sn can be realized by polynomial differential operators. Using this realization, we give a complete classification of irreducible weight sn-modules with finite dimensional weight spaces for any n. All such modules can be clearly characterized by the tensor product of son-modules, sl2-modules and modules over the Weyl algebra.
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