Abstract
The n-th Schrödinger algebra s c h n : = s l 2 ⋉ h n is the semi-direct product of the Lie algebra s l 2 with the n-th Heisenberg Lie algebra h n . In this paper, we classify the s c h n -modules (n ≥ 2) that are free of rank 1 when restricted to the Cartan subalgebra (modulo center). Furthermore, the simplicities of these modules are determined.
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