TL;DR
This paper investigates the arithmetic properties of certain lattices in PU(n,1), revealing a new non-arithmetic lattice in PU(3,1) that is distinct from known examples, expanding understanding of lattice classifications.
Contribution
It introduces a novel non-arithmetic lattice in PU(3,1) that is not commensurable with existing non-arithmetic lattices, providing new insights into lattice diversity.
Findings
Identifies a non-arithmetic lattice in PU(3,1)
Shows this lattice is not commensurable with the Deligne-Mostow lattice
Expands the classification of lattices in complex hyperbolic space
Abstract
We study the arithmeticity of the Couwenberg-Heckman-Looijenga lattices in PU(n,1), and show that they contain a non-arithmetic lattice in PU(3,1) which is not commensurable to the non-arithmetic Deligne-Mostow lattice in PU(3,1).
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