The 290 fixed-point sublattices of the Leech lattice

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.

22 pages, 1 table, latex; 2 supplemental tables (pdf) and 1 data file (text) included in the source file. Version 2 adds a note describing the situation for the E_8 lattice. Version 3 adds data for the lattices as text file readable by the computer algebra system Magma

References in corpus (7)

• Notes on the K3 Surface and the Mathieu group M_24
• Mock Modular Mathieu Moonshine Modules
• Finite groups of symplectic automorphisms of hyperkähler manifolds of type $K{3}^{[2]}$
• Mathieu Moonshine and the Geometry of K3 Surfaces
• Exceptional Algebra and Sporadic Groups at c=12
• Automorphisms of hyperkähler manifolds
• Towards a classification of symplectic automorphisms on manifolds of $K{3}^{[n]}$ type

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