Partition identities and quiver representations. (English) Zbl 1400.05026
Motivated by giving an elementary proof for a family of identities introduced by M. Reineke [J. Inst. Math. Jussieu 9, No. 3, 653–667 (2010; Zbl 1232.53072)], the paper under review presents a specific connection between classical partition combinatorics and the theory of quiver representations. In particular, they prove an analogue of A. L. Cauchy’s Durfee square identity to multipartitions. They use a generalization of the Durfee square to multiple Durfee rectangles. By establishing a weight-preserving bijection between two sets of multipartitions and using the generating series arguments, they obtain the so called quiver Durfee identity.
The authors also use their results to give a new explanation of M. Reineke’s identity in the case of type A quivers.
The authors also use their results to give a new explanation of M. Reineke’s identity in the case of type A quivers.
Reviewer: Donna Q. J. Dou (Changchun)
MSC:
| 05A17 | Combinatorial aspects of partitions of integers |
| 14L30 | Group actions on varieties or schemes (quotients) |
| 16G20 | Representations of quivers and partially ordered sets |
| 05E15 | Combinatorial aspects of groups and algebras (MSC2010) |
Citations:
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