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

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

2008-06-30

arxiv.org/abs/0806.4822v1

Physics

High Energy Physics

High Energy Physics - Theory

Invited talk at The 17th Colloquium "Integrable Systems and Quantum Symmetries", Prague, June 19-21, 2008. Very pedagogical. S

Scientific paper

In 1998 the Adapted Ordering Method was developed for the study of the representation theory of the superconformal algebras in two dimensions. It allows: to determine the maximal dimension for a given type of space of singular vectors, 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 talk I introduce the present version of the Adapted Ordering Method, published in J. Phys. A: Math. Theor. 41 (2008) 045201, which can be applied to general Lie algebras and superalgebras and their generalizations, provided they can be triangulated.

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