2012/03/29 by Valery Gritsenko, Gritsenko, Valery
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Number Theory (math.NT) #Representation Theory (math.RT) #hep-th #math.AG #math.NT #math.RT
paper · pdf · doi:10.48550/arxiv.1203.6503
14 pages
arxiv created 2012/03/29 · arxiv updated 2012/03/30
The fake monster Lie algebra is determined by the Borcherds function Phi12 which is the reflective modular form of the minimal possible weight with respect to O(II2,26). We prove that the first non-zero Fourier-Jacobi coefficient of Phi12 in any of 23 Niemeier cusps is equal to the Weyl-Kac denominator function of the affine Lie algebra of the root system of the corresponding Niemeier lattice. This is an automorphic answer (in the case of the fake monster Lie algebra) on the old question of I. Frenkel and A. Feingold (1983) about possible relations between hyperbolic Kac-Moody algebras, Siegel modular forms and affine Lie algebras.