Representations of Aut(A(Gamma)) acting on homogeneous components of A(Gamma) and A(Gamma) dual

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.