Partition Identities and Quiver Representations

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 $Q$ of Dynkin type $A$ of arbitrary orientation. Our identity is stated in terms of the lacing diagrams of S. Abeasis - A. Del Fra, which parameterize orbits of the representation space of $Q$ for a fixed dimension vector.

26 pages

References in corpus (2)

• On the Cohomological Hall Algebra of Dynkin quivers
• Cohomological Donaldson-Thomas theory of a quiver with potential and quantum enveloping algebras

Cited by in corpus (2)

• Quantum dilogarithm identities for n-cycle quivers
• Interpolating factorizations for acyclic Donaldson--Thomas invariants