2023/01/30 by Yuma Mizuno, Mizuno, Yuma
Computer Science · Mathematics · #11F03 #11P84 #13F60 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Number Theory (math.NT) #Quantum Algebra (math.QA) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2301.13239
openalex publication_date 2023/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We classify periodic Y-systems of rank 2 satisfying the symplectic property. We find that there are six such Y-systems. In all cases, the periodicity follows from the existence of two reddening sequences associated with the time evolution of the Y-systems in positive and negative directions, which gives rise to quantum dilogarithm identities associated with Donaldson-Thomas invariants. We also consider q-series called the Nahm sums associated with these Y-systems. We see that they are included in Zagier's list of rank 2 Nahm sums that are likely to be modular functions. It was recently shown by Wang that they are indeed modular functions.