Abstract
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.
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Translated from Funktsional′nyi Analiz i Ego Prilozheniya, Vol. 52, No. 4, pp. 38–61, 2018
This work was supported by RFBR grant no. 16-01-00818.
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Vinberg, E.B. On Some Free Algebras of Automorphic Forms. Funct Anal Its Appl 52, 270–289 (2018). https://doi.org/10.1007/s10688-018-0237-0
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DOI: https://doi.org/10.1007/s10688-018-0237-0