Symmetry in Nonlinear Mathematical Physics - 2009

Beatriz Gato-Rivera (Instituto de Fisica Fundamental, CSIC, Madrid, Spain)

The adapted ordering method for representation theory

I will introduce the Adapted Ordering Method for Lie algebras and superalgebras, and their generalizations, provided they can be triangulated. This method allows to determine maximal dimensions for a given type of space of singular vectors and to identify all singular vectors by only a few coefficients. As a result, it also facilitates to spot subsingular vectors and to set the basis for constructing embedding diagrams.