Valery Gritsenko (Lille):

Lorentzian Kac-Moody algebras with 2-reflective Weyl groups

In this talk I present some new results which we obtained recently with V. Nikulin (see arXiv:1602.08359). We describe a new large class of Lorentzian Kac-Moody algebras. For all ranks, we classify 2-reflective hyperbolic lattices S with the group of 2-reflections of finite volume and with a lattice Weyl vector. They define the corresponding hyperbolic Kac-Moody algebras which are graded by S. We construct Lorentzian Kac-Moody algebras which give their automorphic corrections: they are graded by the S, have the same simple real roots, but their denominator identities are given by automorphic forms with 2-reflective divisors. We give exact constructions of these automorphic forms for most of the lattices as Borcherds products and, in some cases, as additive Jacobi liftings.
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