Quantum dilogarithms and partition q-series

Abstract

In our previous work [arXiv:1403.6569], we introduced the partition q-series for mutation loop --- a loop in exchange quiver. In this paper, we show that for certain class of mutation sequences, called reverse-ending mutation loops, a graded version of partition q-series essentially coincides with the ordered product of quantum dilogarithm associated with each mutation; the partition q-series provides a state-sum description of combinatorial Donaldson-Thomas invariants introduced by B. Keller.

24 pages, published version

References in corpus (5)

• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Calabi-Yau algebras
• R-Twisting and 4d/2d Correspondences
• Quiver mutation and combinatorial DT-invariants
• Quiver mutation loops and partition q-series