Characteristic rank of vector bundles over Stiefel manifolds

The characteristic rank of a vector bundle $\xi$ over a finite connected $CW$-complex $X$ is by definition the largest integer $k$, $0\leq k\leq $\mathrm{d}\mathrm{i}\mathrm{m}$(X)$,suchthateverycohomologyclass$x\in H^j(X;\mathbb Z_2)$,$0\leq j\leq k$,isapolynomialintheStiefel-Whitneyclasses$w_i(\xi)$. In this note we compute the characteristic rank of vector bundles over the Stiefel manifold $V_k({\mathbb{F}}^n)$, $\mathbb{F}=\mathbb{R},\mathbb{C},\mathbb{H}$.