Harmonic Maaß-Jacobi forms of degree 1 with higher rank indices

Abstract

We define and investigate real analytic weak Jacobi forms of degree 1 and arbitrary rank. En route we calculate the Casimir operator associated to the maximal central extension of the real Jacobi group, which for rank exceeding 1 is of order 4. In ranks exceeding 1, the notions of H-harmonicity and semi-holomorphicity are the same.

28 pages

References in corpus (2)

• Integrable highest weight modules over affine superalgebras and Appell's function
• Higher-Level Appell Functions, Modular Transformations, and Characters

Cited by in corpus (2)

• Gromov-Witten theory of elliptic fibrations: Jacobi forms and holomorphic anomaly equations
• Jacobi Forms of Indefinite Lattice Index