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In 1998 the Adapted Ordering Method was developed for the study of therepresentation theory of the superconformal algebras in two dimensions. Itallows: to determine the maximal dimension for a given type of space ofsingular vectors, to identify all singular vectors by only a few coefficients,to spot subsingular vectors and to set the basis for constructing embeddingdiagrams. In this talk I introduce the present version of the Adapted OrderingMethod, published in J. Phys. A: Math. Theor. 41 (2008) 045201, which can beapplied to general Lie algebras and superalgebras and their generalizations,provided they can be triangulated.

The Adapted Ordering Method for the Representation Theory of Lie Algebras and Superalgebras and their Generalizations