The fake monster algebra and singular Borcherds products
In this paper we consider several problems in the theory of automorphic products and generalized Kac-Moody algebras proposed by Borcherds in 1995. We show that the denominator of the fake monster algebra defines the unique holomorphic Borcherds product of singular weight on a maximal lattice. We giv...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2025
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| In: |
Advances in mathematics
Year: 2025, Volume: 461, Pages: 1-52 |
| ISSN: | 1090-2082 |
| DOI: | 10.1016/j.aim.2024.110083 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.aim.2024.110083 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0001870824005991 
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| Author Notes: | Haowu Wang, Brandon Williams |
| Summary: | In this paper we consider several problems in the theory of automorphic products and generalized Kac-Moody algebras proposed by Borcherds in 1995. We show that the denominator of the fake monster algebra defines the unique holomorphic Borcherds product of singular weight on a maximal lattice. We give a full classification of symmetric holomorphic Borcherds products of singular weight on lattices of prime level. Finally we prove that all twisted denominator identities of the fake monster algebra arise as the Fourier expansions of Borcherds products of singular weight at a certain cusp. The proofs rely on an identification between modular forms for the Weil representation attached to lattices of type U(N)⊕U⊕L and certain tuples of Jacobi forms of level N. |
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| Item Description: | Online verfügbar: 30 December 2024 Gesehen am 13.05.2025 |
| Physical Description: | Online Resource |
| ISSN: | 1090-2082 |
| DOI: | 10.1016/j.aim.2024.110083 |