  We consider the generalization of Kleshchev's lowering operators obtained by
raising all the Carter-Lusztig operators in their definition to a power less
than the characteristic of the ground field. If we apply such an operator to a
nonzero GL_{n-1}-high weight vector of an irreducible representation of GL_n,
shall we get a nonzero GL_{n-1}-high weight vector again? The present paper
gives the explicit answer to this question. In this way we obtain a new
algorithm for generating some normal weights.
