39 research outputs found
Conformal Designs based on Vertex Operator Algebras
We introduce the notion of a conformal design based on a vertex operator
algebra. This notation is a natural analog of the notion of block designs or
spherical designs when the elements of the design are based on self-orthogonal
binary codes or integral lattices, respectively. It is shown that the subspaces
of fixed degree of an extremal self-dual vertex operator algebra form conformal
11-, 7-, or 3-designs, generalizing similar results of Assmus-Mattson and
Venkov for extremal doubly-even codes and extremal even lattices. Other
examples are coming from group actions on vertex operator algebras, the case
studied first by Matsuo. The classification of conformal 6- and 8-designs is
investigated. Again, our results are analogous to similar results for codes and
lattices.Comment: 35 pages with 1 table, LaTe