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 adopted to the situation where the Weyl
denominator becomes singular with respect to a reductive subalgebra. We study
some modifications of the injection fan technique and demonstrate that it is
possible to define the "subtracted fans" that play the role similar to the
original ones. Possible applications of subtracted fans in CFT models are
considered.