A note on singular D-branes in group manifolds

After reviewing the D-branes as a conjugacy classes and various charge quantization (modulo $k$) in WZW model, we develop the classification and systematic construction of all possible untwisted D-branes in Lie groups of A-D-E series. D-branes are classified according to their positions in the maximal torus. The moduli space of D-branes is naturally identified with unit cell in the weight space which is exponentiated to be the maximal torus. However, for the D-brane classification, one may consider only the fundamental Weyl domain that is surrounded by the hyperplanes defined by the Weyl reflection. We construct all D-branes by the method of iterative deletion of the Dynkin diagram. The dimensionality of the D-branes always becomes even number and it reduces as we go from a generic point of the fundamental domain to the higher co-dimensional boundaries. Quantum mechanical stability requires that only D-branes at discrete positions are allowed