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

3 Aug 2022  ·  Manuel K. -H. Müller, Nils R. Scheithauer ·

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. This representation plays an important role in the theory of automorphic forms. We show that its invariants are induced from $5$ fundamental invariants.

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Number Theory