Some free algebras of automorphic forms on symmetric domains of type IV

Some arithmetic quotients of symmetric domains of type IV can be interpreted as moduli varieties of multipolarized K 3 surfaces. Making use of this interpretation, we prove that, for n = 3, 4, 5, 6, 7, some natural algebras of automorphic forms on the n -dimensional symmetric domains of type IV are...

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Bibliographic Details
Published in:Transformation groups 2010-09, Vol.15 (3), p.701-741
Main Author: Vinberg, E. B.
Format: Article
Language:English
Subjects:
Algebra
Lie Groups
Mathematics
Mathematics and Statistics
Topological Groups
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Summary:Some arithmetic quotients of symmetric domains of type IV can be interpreted as moduli varieties of multipolarized K 3 surfaces. Making use of this interpretation, we prove that, for n = 3, 4, 5, 6, 7, some natural algebras of automorphic forms on the n -dimensional symmetric domains of type IV are free, and we find the degrees of their generators. This implies that the corresponding arithmetic groups are generated by complex reflections.
ISSN:1083-4362
1531-586X
DOI:10.1007/s00031-010-9107-4