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Automorphic correction of the hyperbolic Kac-Moody algebra $E_{10}$ (1304.5811v1)
Published 21 Apr 2013 in math.RA, math-ph, math.MP, and math.NT
Abstract: In this paper we study automorphic correction of the hyperbolic Kac-Moody algebra $E_{10}$, using the Borcherds product for O(10,2) attached to a weakly holomorphic modular form of weight -4 for $SL_2(\mathbb Z)$. We also clarify some aspects of automorphic correction for Lorentzian Kac-Moody algebras and give heuristic reasons for the expectation that every Lorentzian Kac-Moody algebra has an automorphic correction.