On Kostant root systems of Lie superalgebras

We study the eigenspace decomposition of a basic classical Lie superalgebra under adjoint action toral subalgebra, thus extending results Kostant. In recognition Kostant's contribution we refer to eigenfunctions appearing in as Kostant roots. then prove that root systems inherit main properties systems. Our approach is combinatorial nature and utilizes certain graphs naturally associated with particular, reprove without making use Killing form.