Refined dynkin data for nilpotent elements

Let B be a Borel subgroup in a complex semisimple Lie group G and let g be the Lie algebra corresponding to G. For each nilpotent element x ∈ g we define an element cl_B(x) of the Cartan algebra of g as a homology class of an appropriate curve on the flag variety G/B. For x "generic" in its G-orbit O the class cl_B(x) coincides with the element defining the weighted Dynkin diagram corresponding to O. We obtain some information about cl_B(x) and, in particular, calculate it completely in the case of regular x.