# Item

ITEM ACTIONSEXPORT

Released

Journal Article

#### The classification of free algebras of orthogonal modular forms

##### External Resource

https://doi.org/10.1112/S0010437X21007429

(Publisher version)

##### Fulltext (public)

2006.02291.pdf

(Preprint), 269KB

##### Supplementary Material (public)

There is no public supplementary material available

##### 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.