On Some Free Algebras of Automorphic Forms

Resumo

It is proved that, for n = 8, 9, 10, the natural algebra of automorphic forms of the group O⁺_2,n(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 ≤ 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.