Pieces of 2d: existence and uniqueness for Barnes–Wall and Ypsilanti lattices

Robert L. Griess
2005 Advances in Mathematics  
We give a new existence proof for the rank 2 d even lattices usually called the Barnes-Wall lattices, and establish new results on uniqueness, structure and transitivity of the automorphism group on certain kinds of sublattices. Our proofs are relatively free of calculations, matrix work and counting, due to the uniqueness viewpoint. We deduce the labeling of coordinates on which earlier constructions depend. Extending these ideas, we construct in dimensions 2 d , for d >> 0,
doi:10.1016/j.aim.2004.08.014 fatcat:6webrednrfa3rdgl4p5en2pwyq