Generalised permutation branes on a product of cosets Gk1/H×Gk2/H

We study the modifications of the generalized permutation branes defined in hep-th/0509153, which are required to give rise to the non-factorizable branes on a product of cosets Gk1/H×Gk2/H. We find that for k1≠k2 there exists big variety of branes, which reduce to the usual permutation branes, when k1=k2 and the permutation symmetry is restored.