Deformations of homogeneous foliations

Let $X$ be a simply connected compact homogeneous Kähler manifold, $b_2(X)=1$, and let $E_\rho$ be a homogeneous vector foliation on $X$. A complete effective family of deformations of a holomorphic vector foliation $E_\rho$, this family parametrized by a neighborhood of zero in $H^1(X,O_{\mathrm{End}E_\rho})$, is constructed.