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 clB(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 clB(x) coincides with the element defining the weighted Dynkin diagram corresponding to O. We obtain some information about clB(x) and, in particular, calculate it completely in the case of regular x.
ASJC Scopus subject areas
- Mathematics (all)