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The Memoirs of the AMS is devoted to the publication of new research in all areas of pure and applied mathematics. The Memoirs is designed particularly to publish long papers of groups of cognate papers in book form, and is under the supervision of the Editorial Committee of the AMS journal Transactions of the American Mathematical Society. All papers are peer-reviewed.
Kaiwen Sun, University of Science and Technology of China, Hefei, People's Republic of China. Haowu Wang, Wuhan University, People's Republic of China. Brandon Williams, Heidelberg University, Germany
Chapters; 1. Introduction; 2. Preliminaries; 3. The hyperbolization of affine Kac-Moody algebras; 4. Root systems associated with reflective Borcherds products of singular weight; 5. The classification of affine Lie algebras with hyperbolizations; 6. The antisymmetric case: holomorphic CFTs of central charge 24; 7. The symmetric case: holomorphic SCFTs of central charge 12; 8. The symmetric case: four exotic CFTs; 9. The 12 symmetric cases: the construction as additive lifts; 10. Fourier expansions of singular-weight reflective Borcherds products; 11. The classification of anti-symmetric root systems; 12. The classification of symmetric root systems; 13. Application: anti-symmetric Siegel paramodular forms of weight 3; 14. Remarks, questions and conjectures; 15. Long tables
