Gelfand-Tsetlin Crystals of Kostant-Kumar modules

We give Gelfand-Tsetlin crystals for the Kostant-Kumar modules for the finite simple Lie algebra of type A. Kostant-Kumar modules are cyclic submodules of the tensor product of two irreducible highest weight modules of a symmetrizable Kac-Moody Lie algebras. In this case (type A), we also provide a polytopal model for Kostant-Kumar modules in terms of BiKogan faces.