Lorentzian Kac-Moody algebras with Weyl groups of 2-reflections

Gritsenko, Valery and Nikulin, Viacheslav V (2018) Lorentzian Kac-Moody algebras with Weyl groups of 2-reflections. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 116 (3). pp. 485-533.

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Abstract

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 of restricted arithmetic type which are graded by S. For most of them, 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 as Borcherds products and, in some cases, as additive Jacobi liftings.

Item Type:	Article
Additional Information:	Var2: 75 pages, 16 figures. The exposition polished, some remarks and references added
Uncontrolled Keywords:	math.AG, math.AG, math.NT, math.QA
Depositing User:	Symplectic Admin
Date Deposited:	10 Apr 2018 06:35
Last Modified:	19 Jan 2023 06:36
DOI:	10.1112/plms.12084
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3019925