  We analyze cyclic cell modules over walled Brauer algebra in terms of a
certain normal form. The latter allows us to decompose the algebra into the
generating set and annihilator ideal of a certain cyclic vector. In addition,
we show that the numbers of reduced basis monomials of given length coincide
with those for the symmetric group. For the semisimple case we utilize the
theory of differential posets to calculate the dimensions of modules in terms
of the paths in Bratelli diagram. It turns out that the number of primitive
idempotents is the same as for the symmetric group.

Representation Theory;Combinatorics