The fake monster algebra and singular Borcherds products

• Verfasst von: Wang, Haowu [VerfasserIn]
• Verfasst von: Williams, Brandon [VerfasserIn]
• Titel: The fake monster algebra and singular Borcherds products
• Verf.angabe: Haowu Wang, Brandon Williams
• Jahr: 2025
• Umfang: 52 S.
• Fussnoten: Online verfügbar: 30 December 2024 ; Gesehen am 13.05.2025
• Titel Quelle: Enthalten in: Advances in mathematics
• Ort Quelle: Amsterdam [u.a.] : Elsevier, 1961
• Jahr Quelle: 2025
• Band/Heft Quelle: 461(2025), Artikel-ID 110083, Seite 1-52
• ISSN Quelle: 1090-2082
• DOI: doi:10.1016/j.aim.2024.110083
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Borcherds products of singular weight
• Sach-SW: Conway's group
• Sach-SW: Fake monster algebra
• Sach-SW: Jacobi forms
• Sach-SW: Leech lattice
• Sach-SW: Modular forms for the Weil representation
• Sach-SW: Twisted denominator identities
• K10plus-PPN: 1925510778

Abstract

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.