Hall polynomials for affine quivers
Abstract
Description
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.
The main alteration is in the last step of the proof of the Main Theorem, since there were difficulties in the original proof using both reflection functors and induction on dimension vector
The main alteration is in the last step of the proof of the Main Theorem, since there were difficulties in the original proof using both reflection functors and induction on dimension vector