Summary: 



ORBITS IN THE LEECH LATTICE



DANIEL ALLCOCK



Abstract. We provide an algorithm for determining whether two
vectors in the Leech lattice are equivalent under its isometry group,
the Conway group Co 0of order ~ 8 x 1018. Our methods rely on
and develop the work of R. T. Curtis, and we describe our in-
tended applications to the symmetry groups of Lorentzian lattices
and the enumeration of lattices of dimension 24 with good prop-
erties such as having small determinant. Our algorithm reduces
the test of equivalence to 4 tests under the subgroup 212:M24,

Source: Allcock, Daniel - Department of Mathematics, University of Texas at Austin

Collections: Mathematics