Hall polynomials for affine quivers

Hubery, Andrew

doi:10.1090/S1088-4165-10-00374-2

Hall polynomials for affine quivers
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by Andrew Hubery

Represent. Theory 14 (2010), 355-378

DOI: https://doi.org/10.1090/S1088-4165-10-00374-2

Published electronically: April 30, 2010

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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.

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