Vertex Operator Superalgebras and Their Representations
Abstract
After giving some definitions for vertex operator SUPERalgebras and their modules, we construct an associative algebra corresponding to any vertex operator superalgebra, such that the representations of the vertex operator algebra are in onetoone correspondence with those of the corresponding associative algebra. A way is presented to decribe the fusion rules for the vertex operator superalgebras via modules of the associative algebra. The above are generalizations of Zhu's constructions for vertex operator algebras. Then we deal in detail with vertex operator superalgebras corresponding to NeveuSchwarz algebras, super affine KacMoody algebras, and free fermions. We use the machinery established above to find the rationality conditions, classify the representations and compute the fusion rules. In the appendix, we present explicit formulas for singular vectors and defining relations for the integrable representations of super affine algebras. These formulas are not only crucial for the theory of the corresponding vertex operator superalgebras and their representations, but also of independent interest.
 Publication:

arXiv eprints
 Pub Date:
 December 1993
 arXiv:
 arXiv:hepth/9312065
 Bibcode:
 1993hep.th...12065K
 Keywords:

 High Energy Physics  Theory;
 Mathematics  Quantum Algebra
 EPrint:
 50 pages, to appear in Contemporary Mathematics