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arXiv · 1910.05226

The D_8-tower of weak Jacobi forms and applications

Dmitry Adler·Valery Gritsenko
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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.

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Dmitry Adler, Valery Gritsenko. 2019-10-11. The D_8-tower of weak Jacobi forms and applications. https://doi.org/10.1016/j.geomphys.2020.103616

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