A quiver mutation loop is a sequence of mutations and vertexrelabelings, along which a quiver transforms back to the originalform. For a given mutation loop γ, we introduce a quantity called a partition q-seriesZγ which takes values in (Formula presented.) where (Formula presented.) is some positive integer. Thepartition q-series are invariant under pentagon moves. If thequivers are of Dynkin type or square products thereof, theyreproduce so-called fermionic or quasi-particle character formulasof certain modules associated with affine Lie algebras. They enjoynice modular properties as expected from the conformal field theorypoint of view.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics