  In this paper we will study the structure of algebras A(Gamma) associated to
two directed, layered graphs Gamma. These are algebras associated with Hasse
graphs of n-gons and the algebras Q_n related to pseudoroots of noncommutative
polynomials. We will find the filtration preserving automorphism group of these
algebras and then we will find the multiplicities of the irreducible
representations of Aut(A(Gamma)) acting on the homogeneous components of
A(Gamma) and A(Gamma) dual.
