Automorphic correction of the hyperbolic Kac-Moody algebra E10

Abstract

In this paper, we study automorphic correction of the hyperbolic Kac-Moody algebra E10, using the Borcherds product for O(10, 2) attached to a weakly holomorphic modular form of weight −4 for \documentclass[12pt]{minimal}\begin{document}$SL_2(\mathbb {Z})$\end{document}SL2(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.