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- Title
Quiver Mutation Loops and Partition q-Series.
- Authors
Kato, Akishi; Terashima, Yuji
- 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.
- Subjects
LOOPS (Group theory); PARTITIONS (Mathematics); Q-series; MATHEMATICAL sequences; INTEGERS
- Publication
Communications in Mathematical Physics, 2015, Vol 336, Issue 2, p811
- ISSN
0010-3616
- Publication type
Article
- DOI
10.1007/s00220-014-2224-5