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Journal Article

The classification of free algebras of orthogonal modular forms

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Wang,  Haowu
Max Planck Institute for Mathematics, Max Planck Society;

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Fulltext (public)

2006.02291.pdf
(Preprint), 269KB

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Citation

Wang, H. (2021). The classification of free algebras of orthogonal modular forms. Compositio Mathematica, 157(9), 2026-2045. doi:10.1112/S0010437X21007429.


Cite as: http://hdl.handle.net/21.11116/0000-0009-2556-D
Abstract
We prove a necessary and sufficient condition for the graded algebra of automorphic forms on a symmetric domain of type IV to be free. From the necessary condition, we derive a classification result. Let $M$ be an even lattice of signature $(2,n)$ splitting two hyperbolic planes. Suppose $\Gamma$ is a subgroup of the integral orthogonal group of $M$ containing the discriminant kernel. It is proved that there are exactly 26 groups $\Gamma$ such that the space of modular forms for $\Gamma$ is a free algebra. Using the sufficient condition, we recover some well-known results.