  Let g be a complex simple Lie algebra and h a Cartan subalgebra. The Clifford
algebra C(g) of g admits a Harish-Chandra map. Kostant conjectured (as
communicated to Bazlov in about 1997) that the value of this map on a (suitably
chosen) fundamental invariant of degree 2m+1 is just the zero weight vector of
the simple 2m+1-dimensional module of the principal s-triple obtained from the
Langlands dual of g. Bazlov settled this conjecture positively in type A.
  The Kostant conjecture was reformulated (Alekseev-Bazlov-Rohr) in terms of
the Harish-Chandra map for the enveloping algebra U(g) composed with evaluation
at the half sum of the positive roots.
  In an earlier work we settled an analogue of the Kostant conjecture obtained
by replacing the Harish-Chandra map by a "generalized Harish-Chandra" map whose
image is described via Zhelobenko invariants. Here we show that there are
analogue Zhelobenko invariants which describe the image of the Harish-Chandra
map. Following this a similar proof goes through.

Representation Theory