Abstract
A quiver mutation loop is a sequence of mutations and vertex relabelings, along which a quiver transforms back to the original form. For a given mutation loop \(\gamma\), we introduce a quantity called a partition q-series \({Z(\gamma)}\) which takes values in \({\mathbb{N}[[q^{1/ \Delta}]]}\) where \(\Delta\) is some positive integer. The partition q-series are invariant under pentagon moves. If the quivers are of Dynkin type or square products thereof, they reproduce so-called fermionic or quasi-particle character formulas of certain modules associated with affine Lie algebras. They enjoy nice modular properties as expected from the conformal field theory point of view.
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Communicated by P. T. Chruściel
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Kato, A., Terashima, Y. Quiver Mutation Loops and Partition q-Series. Commun. Math. Phys. 336, 811–830 (2015). https://doi.org/10.1007/s00220-014-2224-5
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DOI: https://doi.org/10.1007/s00220-014-2224-5