  In the representation theory of simple Lie algebras, we consider the problem
of constructing a monomial basis in an arbitrary irreducible finite-dimensional
highest weight module. We construct a PBW-type basis in every
finite-dimensional representation of $B_n$ and $D_n$ and we describe the
associated semigroup of essential signatures. These bases are parameterized by
integer points in some polytopes. We give the inequalities defining these
polytopes.
