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This article is cited in 4 scientific papers (total in 5 papers)
On Some Free Algebras of Automorphic Forms
È. B. Vinberg Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
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, moduli space, period map.
Received: 05.04.2018
Citation:
È. B. Vinberg, “On Some Free Algebras of Automorphic Forms”, Funktsional. Anal. i Prilozhen., 52:4 (2018), 38–61; Funct. Anal. Appl., 52:4 (2018), 270–289
Linking options:
https://www.mathnet.ru/eng/faa3583https://doi.org/10.4213/faa3583 https://www.mathnet.ru/eng/faa/v52/i4/p38
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Abstract page: | 425 | Full-text PDF : | 52 | References: | 46 | First page: | 31 |
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