Hall polynomials for affine quivers

Mathematics – Representation Theory

Scientific paper

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The main alteration is in the last step of the proof of the Main Theorem, since there were difficulties in the original proof

Scientific paper

We use the comultiplication to prove that Hall polynomials exist for all finite and affine quivers. In the finite and cyclic cases, this approach provides a new and simple proof of the existence of Hall polynomials. In general, these polynomials are defined with respect to the decomposition classes of Bongartz and Dudek, a generalisation of the Segre classes for square matrices.

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