On the representation rings of quivers of exceptional Dynkin type.
In the paper the representation ring \(R(\mathbb{E}_6)\) of the Dynkin quiver \(\mathbb{E}_6\) is investigated. The representation ring \(R(Q)\) of a quiver \(Q\) encodes direct sums and tensor products of representations of the quiver \(Q\). The author presents methods which allow to reduce the computation of parts of \(R(Q)\) to the computation of \(R(Q')\) for connected subquivers \(Q'\) of \(Q\). Developing these methods the author computes and gives an explicit description of the representation ring \(R(\mathbb{E}_6)\) (for all orientations of \(\mathbb{E}_6\)). Moreover, there is explained how one can apply these methods (presented in the paper) to compute representation rings of \(\mathbb{E}_7\) and \(\mathbb{E}_8\).
scientific article; zbMATH DE number 5300470