TY - JOUR

T1 - Quiver Mutation Loops and Partition q-Series

AU - Kato, Akishi

AU - Terashima, Yuji

N1 - Publisher Copyright:
© 2014, Springer-Verlag Berlin Heidelberg.

PY - 2015/6

Y1 - 2015/6

N2 - 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.

AB - 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.

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U2 - 10.1007/s00220-014-2224-5

DO - 10.1007/s00220-014-2224-5

M3 - Article

AN - SCOPUS:84925489081

SN - 0010-3616

VL - 336

SP - 811

EP - 830

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

IS - 2

ER -