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Representation Theory

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Hall polynomials for affine quivers

Author: Andrew Hubery
Journal: Represent. Theory 14 (2010), 355-378
MSC (2010): Primary 16G20
Published electronically: April 30, 2010
MathSciNet review: 2644456
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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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Andrew Hubery
Affiliation: Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, United Kingdom

Received by editor(s): October 8, 2007
Published electronically: April 30, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.