  Let g be the complex semisimple Lie algebra associated to a complex
semisimple algebraic group G, b a Borel subalgebra of g, h the Cartan
sublagebra contained in b and N the unipotent subgroup of G corresponding to
the nilradical n of b. We show that the explicit formula for the extremal
projection operator for g obtained by Asherova, Smirnov and Tolstoy and similar
formulas for Zhelobenko operators are related to the existence of a birational
equivalence N\times h -> b given by the restriction of the adjoint action.
Simple geometric proofs of formulas for the "classical" counterparts of the
extremal projection operator and of Zhelobenko operators are also obtained.
