Partition identities and quiver representations |
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Authors: | Richárd Rimányi Anna Weigandt Alexander Yong |
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Affiliation: | 1.Department of Mathematics,The University of North Carolina at Chapel Hill,Chapel Hill,USA;2.Department of Mathematics,University of Illinois at Urbana-Champaign,Urbana,USA |
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Abstract: | We present a particular connection between classical partition combinatorics and the theory of quiver representations. Specifically, we give a bijective proof of an analogue of A. L. Cauchy’s Durfee square identity to multipartitions. We then use this result to give a new proof of M. Reineke’s identity in the case of quivers ({mathcal {Q}}) of Dynkin type A. Our identity is stated in terms of the lacing diagrams of S. Abeasis–A. Del Fra, which parameterize orbits of the representation space of ({mathcal {Q}}) for a fixed dimension vector. |
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