On the vector fields on an algebraic homogeneous space (Q1062189)

Let G be a simply-connected complex semisimple Lie group, P a parabolic subgroup of G and T a maximal torus contained in P; let V denote the holomorphic vector field on G/P obtained by exponentiating a regular element of Lie(T). The author calculates the Chern classes of a homogeneous vector bundle on G/P on the zero set of V. The principal methods used are those of \textit{J. B. Carrell} and \textit{D. I. Lieberman} [Math. Ann. 225, 263-273 (1977; Zbl 0365.32020)] whose results are reviewed in the first part of this paper.