Coxeter groups, Lorentzian lattices, and K3 surfaces

TL;DR

This paper investigates the structure of Coxeter groups to determine automorphism groups of Lorentzian lattices and K3 surfaces, providing new insights into their symmetries and algebraic properties.

Contribution

It introduces methods to compute automorphism groups of Lorentzian lattices and K3 surfaces using Coxeter group normalizers, extending previous understanding of their symmetries.

Findings

Computed automorphism groups of specific Lorentzian lattices

Determined automorphism groups of certain K3 surfaces

Established a link between Coxeter group normalizers and geometric symmetries

Abstract

The main result of this paper describes the normalizer of a finite parabolic subgroup of a (possibly infinite) Coxeter group. We use this to compute the automorphism groups of some Lorentzian lattices and K3 surfaces.