The 290 fixed-point sublattices of the Leech lattice

2015/05/31 by Gerald Hoehn, Geoffrey Mason · 1 citation
Mathematics · Physics and Astronomy · #math.GR #hep-th #math.AG

paper · pdf · doi:10.1016/j.jalgebra.2015.08.028

published as J. of Algebra, 448 (2016), 618-637 · 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

arxiv created 2016/01/13 · arxiv updated 2016/01/18

Abstract

We determine the orbits of fixed-point sublattices of the Leech lattice with respect to the action of the Conway group Co₀. 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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