Hall polynomials for affine quivers

Abstract

We use Green’s comultiplication formula to prove that Hall polynomials exist for all Dynkin and affine quivers. For Dynkin and cyclic quivers this approach provides a new and simple proof of the existence of Hall polynomials. For non-cyclic affine quivers these polynomials are defined with respect to the decomposition classes of Bongartz and Dudek, a generalisation of the Segre classes for square matrices.