On the representation rings of quivers of exceptional Dynkin type

The direct sum and tensor product (defined point-wise and arrow-wise) of representations of a given quiver is encoded in the representation ring of that quiver. We provide methods which reduce the computation of certain parts of the representation ring of a quiver to that of connected subquivers. These methods, combined with known results on the representation rings of quivers of type A and D, and supplemented by certain matrix calculations, yield an explicit description of the representation rings of all quivers of type E6.