Time: April 19, 2024 (Friday)  15:00-16:00

Speaker: Prof. Haowu Wang (Wuhan Univ)

Inviter: Prof. Daxin Xu

Place: MCM510

Title: Hyperbolization of affine Lie algebras

Abstract: In 1983, Feingold and Frenkel posed a question about possible relations between affine Lie algebras, hyperbolic Kac--Moody algebras and Siegel modular forms. We give an automorphic answer to this question and its generalization. We classify Borcherds--Kac--Moody algebras whose denominators define reflective automorphic products of singular weight. As a consequence, we prove that there are exactly 81 affine Lie algebras which have nice extensions to BKM algebras. We find that 69 of them appear in Schellekens’ list of holomorphic CFT of central charge 24, while 8 of them correspond to the N=1 structures of holomorphic SCFT of central charge 12 composed of 24 chiral fermions. The last 4 cases are related to exceptional modular invariants from nontrivial automorphisms of fusion algebras. This clarifies the relationship of affine Lie algebras, vertex algebras and hyperbolic BKM superalgebras at the level of modular forms. This is based on a joint paper with Kaiwen Sun and Brandon Williams.