Recursive algorithm and branching for nonmaximal embeddings

TL;DR

This paper develops a recursive algorithm using the injection fan technique to compute branching coefficients in affine Lie algebra modules, including singular cases, with potential applications in conformal field theory.

Contribution

It introduces a general injection fan-based method for calculating branching coefficients in affine Lie algebras, handling singular Weyl denominators and applicable to any reductive subalgebra.

Findings

Established a recursive relation for branching coefficients

Defined the injection fan and Weyl numerator for singular cases

Demonstrated applications in conformal field theory models

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.