Conformal designs based on vertex operator algebras

• Autores: Gerald Höhn
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 217, Nº 5, 2008, págs. 2301-2335
• Idioma: inglés
• DOI: 10.1016/j.aim.2007.11.003
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• Resumen

  • 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 an extremal self-dual vertex operator algebra of fixed degree form conformal 11-, 7-, or 3-designs, generalizing similar results of Assmus and 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.