The Adapted Ordering Method in Representation Theory

Details The Adapted Ordering Method in Representation Theory The Adapted Ordering Method in Representation Theory

2004-10-15

arxiv.org/abs/hep-th/0410172v2

Physics

High Energy Physics

High Energy Physics - Theory

Several improvements in the redaction. Conclusions and references added. Latex, 11 pages

Scientific paper

In 1998 the Adapted Ordering Method was developed for the representation theory of the superconformal algebras. This method, which proves to be very powerful, can be applied to most algebras and superalgebras, however. It allows: to determine maximal dimensions for a given type of singular vector space, to identify all singular vectors by only a few coefficients, to spot subsingular vectors and to set the basis for constructing embedding diagrams. In this article we present the Adapted Ordering Method for general algebras and superalgebras which admit a triangulation and review briefly the results obtained for the Virasoro algebra and for the N=2 and Ramond N=1 superconformal algebras.

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