Abstract
The relation between the dimensions of indecomposable representations of polyquivers of tame type and the roots of the corresponding extended Dynkin diagrams is studied. It is proved that dimensions with infinitely many indecomposable representations have the form and dimensions with finitely many indecomposable representations the form or tξ where ξ is the smallest imaginary root, β is a real root smaller than is a natural constant determined by the diagram,m is an arbitrary natural number, and t is a natural number not divisible by . For diagrams different from BAl, and CAl, is equal to the connection number of the diagram, and the dimensions of the indecomposable representations agree with the roots.
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