The 290 fixed-point sublattices of the Leech lattice
Gerald Hoehn, Geoffrey Mason
TL;DR
This paper classifies and details the 290 fixed-point sublattices of the Leech lattice under the action of the Conway group, providing comprehensive data on their structure and symmetries.
Contribution
It explicitly enumerates and describes all fixed-point sublattices of the Leech lattice under the Conway group, including their stabilizers and related lattices.
Findings
Identified 290 fixed-point sublattice orbits
Provided detailed classifications and tables
Analyzed stabilizer subgroups and coinvariant lattices
Abstract
We determine the orbits of fixed-point sublattices of the Leech lattice with respect to the action of the Conway group Co_0. There are 290 such orbits. Detailed information about these lattices, the corresponding coinvariant lattices, and the stabilizing subgroups, is tabulated in several tables.
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