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arXiv · 2208.01921

The invariants of the Weil representation of $\mathrm{SL}_2(\mathbb{Z})$

Manuel K. -H. Müller·Nils R. Scheithauer
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Abstract

The transformation behaviour of the vector valued theta function of a positive-definite even lattice under the metaplectic group $\mathrm{Mp}_2(\mathbb{Z})$ is described by the Weil representation. We show that the invariants of this representation are induced from $5$ fundamental invariants. As an application we give simple generating sets for Jacobi forms of singular weight.

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Manuel K. -H. Müller, Nils R. Scheithauer. 2022-08-03. The invariants of the Weil representation of $\mathrm{SL}_2(\mathbb{Z})$. https://arxiv.org/abs/2208.01921

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