Remarks on the theta decomposition of vector-valued Jacobi forms

TL;DR

This paper investigates the theta decomposition of vector-valued Jacobi forms with nonintegral lattice index, focusing on representations linked to Weil representations of even lattices, and explores potential applications.

Contribution

It introduces a new analysis of theta decomposition for Jacobi forms with nonintegral index related to Weil representations, suggesting novel applications.

Findings

Enhanced understanding of theta decomposition in nonintegral lattice contexts

Potential applications in the theory of Weil representations and lattice theory

New insights into vector-valued Jacobi forms

Abstract

We study the theta decomposition of Jacobi forms of nonintegral lattice index for a representation that arises in the theory of Weil representations associated to even lattices, and suggest possible applications.