Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 3 (2007), 008, 13 pages      math.QA/0610322      http://dx.doi.org/10.3842/SIGMA.2007.008
Contribution to the Proceedings of the O'Raifeartaigh Symposium

The Virasoro Algebra and Some Exceptional Lie and Finite Groups

Michael P. Tuite
Department of Mathematical Physics, National University of Ireland, Galway, Ireland

Received October 09, 2006, in final form December 16, 2006; Published online January 08, 2007

Abstract
We describe a number of relationships between properties of the vacuum Verma module of a Virasoro algebra and the automorphism group of certain vertex operator algebras. These groups include the Deligne exceptional series of simple Lie groups and some exceptional finite simple groups including the Monster and Baby Monster.

Key words: vertex operator algebras; Virasoro algebras; Deligne exceptional series; Monster group.

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