Recursive algorithm and branching for nonmaximal embeddings

Abstract

Recurrent relations for branching coefficients in affine Lie algebras integrable highest weight modules are studied. The decomposition algorithm based on the injection fan technique is developed for the case of an arbitrary reductive subalgebra. In particular we consider the situation where the Weyl denominator becomes singular with respect to the subalgebra. We demonstrate that for any reductive subalgebra it is possible to define the injection fan and the analogue of the Weyl numerator - the tools that describe explicitly the recurrent properties of branching coefficients. Possible applications of the fan technique in CFT models are considered.

LaTeX, 23 pages, 13 figures, section 2 is clarified, new lemma and theorem are introduced, figures are improved, submitted to Journal of Physics A: Mathematical and Theoretical

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• Splints of root systems for special Lie subalgebras
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• Recursive properties of branching and BGG resolution
• On affine extension of splint root systems