Geodesic
On Some Free Algebras of Automorphic Forms
Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 4, pp. 38-61

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It is proved that, for $n=8,9,10$, the natural algebra of automorphic forms of the group $O^+_{2,n}(\mathbb{Z})$ acting on the $n$-dimensional symmetric domain of type IV is free, and the weights of generators are found. This extends results obtained in the author's previous paper for $n\le 7$. On the other hand, as proved in a recent joint paper of the author and O. V. Shvartsman, similar algebras of automorphic forms cannot be free for $n>10$.
Keywords: symmetric domain, automorphic form, reflection group, $K3$-surface, period map.
Mots-clés : moduli space 
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     author = {\`E. B. Vinberg},
     title = {On {Some} {Free} {Algebras} of {Automorphic} {Forms}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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È. B. Vinberg. On Some Free Algebras of Automorphic Forms. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 4, pp. 38-61. http://geodesic.mathdoc.fr/item/FAA_2018_52_4_a2/