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

TL;DR

This paper investigates the automorphism groups of certain graph-related algebras and analyzes how these groups act on the algebra's homogeneous components, revealing their structure and representation multiplicities.

Contribution

It determines the automorphism groups of algebras associated with layered graphs and computes the multiplicities of irreducible representations on their homogeneous components.

Findings

Automorphism groups of A(Gamma) are explicitly characterized.

Multiplicities of irreducible representations are computed.

Results apply to algebras from Hasse graphs and noncommutative polynomial pseudoroots.

Abstract

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.