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.
\Bibitem{Vin18}
\by \`E.~B.~Vinberg
\paper On Some Free Algebras of Automorphic Forms
\jour Funktsional. Anal. i Prilozhen.
\yr 2018
\vol 52
\issue 4
\pages 38--61
\mathnet{http://mi.mathnet.ru/faa3583}
\crossref{https://doi.org/10.4213/faa3583}
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\transl
\jour Funct. Anal. Appl.
\yr 2018
\vol 52
\issue 4
\pages 270--289
\crossref{https://doi.org/10.1007/s10688-018-0237-0}
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This publication is cited in the following 7 articles:
Haowu Wang, Brandon Williams, “Simple lattices and free algebras of modular forms”, Advances in Mathematics, 413 (2023), 108835
H. Wang, B. Williams, “Projective spaces as orthogonal modular varieties”, Transformation Groups, 2022
D. V. Alekseevskii, M. V. Belolipetsky, S. G. Gindikin, V. G. Kac, D. I. Panyushev, D. A. Timashev, O. V. Shvartsman, A. G. Elashvili, O. S. Yakimova, “Èrnest Borisovich Vinberg (obituary)”, Russian Math. Surveys, 76:6 (2021), 1123–1135
Haowu Wang, “The classification of free algebras of orthogonal modular forms”, Compositio Math., 157:9 (2021), 2026
H. Wang, B. Williams, “On some free algebras of orthogonal modular forms”, Adv. Math., 373 (2020), 107332
E. S. Stuken, “Svobodnye algebry avtomorfnykh form Gilberta”, Funkts. analiz i ego pril., 53:1 (2019), 49–66
E. S. Stuken, “Free Algebras of Hilbert Automorphic Forms”, Funct Anal Its Appl, 53:1 (2019), 37
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