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arXiv · 2006.02291

The classification of free algebras of orthogonal modular forms

Haowu Wang
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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.

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Haowu Wang. 2020-06-03. The classification of free algebras of orthogonal modular forms. https://doi.org/10.1112/s0010437x21007429

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