  We study the PBW filtration on irreducible finite--dimensional
representations for the Lie algebra of type $\tt B_n$. We prove in several
cases, including all multiples of the adjoint representation and all
irreducible finite--dimensional representations for $\tt B_3$, that there
exists a normal polytope such that the lattice points of this polytope
parametrize a basis of the corresponding associated graded space. As a
consequence we obtain several classes of favourable modules and graded
combinatorial character formulas.

Representation Theory;Combinatorics