Abstract :
For each self-orthogonal ternary code image of length k, one can obtain an untwisted positive definite integral even lattice image by gluing k copies of the root lattice of type A2 with image as the glue code. Under the assumption that image contains (1,…,1), we construct an untwisted space and two twisted spaces associated with a special lattice containing image as an index 3 sublattice. All nine untwisted and twisted subspaces associated with the cosets of image in L are irreducible modules of the vertex operator algebra associated with image, and they provide different realizations of sl(3, image). Using these realizations of sl(3, image), we construct an analogue of “vertex operator triality”: a beautiful and important phenomenon found by Frenkel, Lepowsky and Meurman in their work on construction of the moonshine representation of the Monster group.
