The invariants of the Weil representation of SL₂(ℤ)

2022/08/03 by Müller, Manuel K. -H., Scheithauer, Nils R.
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2208.01921

Abstract

The transformation behaviour of the vector valued theta function of a positive-definite even lattice under the metaplectic group Mp₂(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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