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Funktsional. Anal. i Prilozhen., 2018, Volume 52, Issue 4, Pages 38–61 (Mi faa3583)  

This article is cited in 1 scientific paper (total in 1 paper)

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.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-01-00818


DOI: https://doi.org/10.4213/faa3583

Full text: PDF file (304 kB)
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English version:
Functional Analysis and Its Applications, 2018, 52:4, 270–289

Bibliographic databases:

UDC: 512.817+515.178.7
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

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. S. Stuken, “Svobodnye algebry avtomorfnykh form Gilberta”, Funkts. analiz i ego pril., 53:1 (2019), 49–66  mathnet  crossref  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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