Lowest weight modules of \(\widetilde{\mathrm{Sp}_{2n}(\mathbb R)}\) of minimal Gelfand-Kirillov dimension
This paper gives a classification of the irreducible lowest weight modules of the metaplectic group with Gelfand-Kirillov dimension \(n\). It is known that there are only four unitary ones with Gelfand-Kirillov dimension \(n\), also known as the minimal representations, namely, the two irreducible constituents of the oscillator representation and their duals. The main result is a criterion on the lowest weights for which the corresponding module is of GK dimension \(n\). It is also proved that these modules occur as submodules of the oscillator representation tensoring with a finite dimensional representation in the sense of Zuckerman.
scientific article; zbMATH DE number 5277628