The D_8-tower of weak Jacobi forms and applications
Abstract
We construct a tower of arithmetic generators of the bigraded polynomial ring J_{*,*}^{w, O}(D_n) of weak Jacobi modular forms invariant with respect to the full orthogonal group O(D_n) of the root lattice D_n for 2\le n\le 8. This tower corresponds to the tower of strongly reflective modular forms on the orthogonal groups of signature (2,n) which determine the Lorentzian Kac-Moody algebras related to the BCOV (Bershadsky-Cecotti-Ooguri-Vafa)-analytic torsions. We prove that the main three generators of index one of the graded ring satisfy a special system of modular differential equations. We found also a general modular differential equation of the generator of weight 0 and index 1 which generates the automorphic discriminant of the moduli space of Enriques surfaces.
Keywords
Cite
@article{arxiv.1910.05226,
title = {The D_8-tower of weak Jacobi forms and applications},
author = {Dmitry Adler and Valery Gritsenko},
journal= {arXiv preprint arXiv:1910.05226},
year = {2020}
}