  Let E be a simple finite dimensional representation of a semisimple Lie
algebra with extremal weight nu and choose nonzero e in E_{nu}. Let M(tau) be
the Verma module with highest weight tau and v_{tau} in M(tau)_{tau} its
canonical generator. We investigate the projection of e \otimes v_{tau} in E
\otimes M(tau) on the central character chi(tau + nu). This is a rational
function in tau and we calculate its poles and zeros. We then apply this result
in order to compare translation functors.
